My paper "Machine learning discovers new champion codes", joint with Yang-Hui He, Q Le, and Dmitrii Riabchenko, was published in Nature's Artificial Intelligence.
www.nature.com/articles/s44...
#MathSky #MachineLearning #CodingTheory
www.nature.com/articles/s44...
#MathSky #MachineLearning #CodingTheory
Machine learning discovers new champion codes - npj Artificial Intelligence
npj Artificial Intelligence - Machine learning discovers new champion codes
www.nature.com
March 28, 2026 at 11:59 AM
My paper "Machine learning discovers new champion codes", joint with Yang-Hui He, Q Le, and Dmitrii Riabchenko, was published in Nature's Artificial Intelligence.
www.nature.com/articles/s44...
#MathSky #MachineLearning #CodingTheory
www.nature.com/articles/s44...
#MathSky #MachineLearning #CodingTheory
Establishes sufficient and necessary conditions for multi-twist Reed-Solomon codes to be self-orthogonal, enabling explicit construction of quantum stabilizer codes achieving the quantum Singleton bound.
#QuantumErrorCorrection #CodingTheory #Research
#QuantumErrorCorrection #CodingTheory #Research
Self-Orthogonal Twisted Reed-Solomon Codes and Quantum Error Correction
arxiv.org
May 25, 2026 at 2:19 PM
Establishes sufficient and necessary conditions for multi-twist Reed-Solomon codes to be self-orthogonal, enabling explicit construction of quantum stabilizer codes achieving the quantum Singleton bound.
#QuantumErrorCorrection #CodingTheory #Research
#QuantumErrorCorrection #CodingTheory #Research
Establishes Fourier-based conditions for local unitary equivalence of orthogonal arrays and irredundant orthogonal arrays, connecting LU equivalence to coding theory duality for linear codes over prime fields.
#QuantumEntanglement #CodingTheory #Research
#QuantumEntanglement #CodingTheory #Research
Local Unitary Equivalence of Orthogonal Arrays and Coding Theory Connections
arxiv.org
September 18, 2026 at 8:37 AM
Establishes Fourier-based conditions for local unitary equivalence of orthogonal arrays and irredundant orthogonal arrays, connecting LU equivalence to coding theory duality for linear codes over prime fields.
#QuantumEntanglement #CodingTheory #Research
#QuantumEntanglement #CodingTheory #Research
Framework for quantum stabilizer codes over Gaussian integer rings, revealing distinct roles of logical and syndrome quotients in error correction with new cardinality formulas and syndrome-based recovery procedures.
#QuantumErrorCorrection #CodingTheory #Research
#QuantumErrorCorrection #CodingTheory #Research
CSS-Type Quantum Error Correction Codes over Gaussian Integer Rings
iq.fp2.dev
September 16, 2026 at 7:53 AM
Framework for quantum stabilizer codes over Gaussian integer rings, revealing distinct roles of logical and syndrome quotients in error correction with new cardinality formulas and syndrome-based recovery procedures.
#QuantumErrorCorrection #CodingTheory #Research
#QuantumErrorCorrection #CodingTheory #Research
Discovers infinite families of 3-designs from linear and nonlinear codes with applications to quantum error-correcting codes and distributed storage systems, achieving optimal locality and distance properties.
#CodingTheory #QuantumErrorCorrection #Research
#CodingTheory #QuantumErrorCorrection #Research
Infinite Families of 3-Designs from Linear and Nonlinear Codes
arxiv.org
September 15, 2026 at 9:19 PM
Discovers infinite families of 3-designs from linear and nonlinear codes with applications to quantum error-correcting codes and distributed storage systems, achieving optimal locality and distance properties.
#CodingTheory #QuantumErrorCorrection #Research
#CodingTheory #QuantumErrorCorrection #Research
Determined Hermitian hull dimensions for (L,P)-TGRS codes and constructed new entanglement-assisted quantum error-correcting codes with flexible parameters through complete case analysis.
#QuantumErrorCorrection #CodingTheory #Research
#QuantumErrorCorrection #CodingTheory #Research
Hermitian Hull Dimensions of (L,P)-Twisted Generalized Reed-Solomon Codes
arxiv.org
July 7, 2026 at 11:40 AM
Determined Hermitian hull dimensions for (L,P)-TGRS codes and constructed new entanglement-assisted quantum error-correcting codes with flexible parameters through complete case analysis.
#QuantumErrorCorrection #CodingTheory #Research
#QuantumErrorCorrection #CodingTheory #Research
Researchers proved vector trifferent codes satisfy |C| ≤ (√2+o(1))·(3/2)^n, tightening the factor 2, and showed improvement |C| ≲ n^{-1/4}·(3/2)^n. Read more: https://getnews.me/new-upper-bound-for-vector-trifferent-codes-improves-classical-limits/ #vectortrifferent #codingtheory
October 7, 2025 at 10:25 PM
Researchers proved vector trifferent codes satisfy |C| ≤ (√2+o(1))·(3/2)^n, tightening the factor 2, and showed improvement |C| ≲ n^{-1/4}·(3/2)^n. Read more: https://getnews.me/new-upper-bound-for-vector-trifferent-codes-improves-classical-limits/ #vectortrifferent #codingtheory
Extended algebraic geometry codes can achieve length q + 1 + 2g√q, and their covering radius has exactly g + 2 possible values (only two when genus = 1). https://getnews.me/extended-algebraic-geometry-codes-dual-and-covering-radii-insights/ #algebraicgeometry #codingtheory
September 29, 2025 at 8:36 AM
Extended algebraic geometry codes can achieve length q + 1 + 2g√q, and their covering radius has exactly g + 2 possible values (only two when genus = 1). https://getnews.me/extended-algebraic-geometry-codes-dual-and-covering-radii-insights/ #algebraicgeometry #codingtheory
Researchers define (*)-(L,P)-twisted generalized Reed‑Solomon (TGRS) codes and present four new linear complementary dual (LCD) code families. Read more: https://getnews.me/researchers-introduce-l-p-twisted-reed-solomon-lcd-codes/ #codingtheory #lcdcodes #reedsolomon
September 19, 2025 at 11:50 PM
Researchers define (*)-(L,P)-twisted generalized Reed‑Solomon (TGRS) codes and present four new linear complementary dual (LCD) code families. Read more: https://getnews.me/researchers-introduce-l-p-twisted-reed-solomon-lcd-codes/ #codingtheory #lcdcodes #reedsolomon
Two ENCODE doctoral candidates made a video introduction to #CodingTheory with ISBN codes as example:
Introduction to Coding Theory: ISBN Code explained (Part 1/2)
YouTube video by AliceandBob
www.youtube.com
December 5, 2024 at 12:35 PM
Two ENCODE doctoral candidates made a video introduction to #CodingTheory with ISBN codes as example:
Overview: A Hacker News discussion explored "Essential Coding Theory" (PDF), clarifying "coding" as error-correcting codes within information theory. It linked these concepts to data compression and AI, and offered supplementary learning resources. #CodingTheory 1/6
August 30, 2025 at 7:00 PM
Overview: A Hacker News discussion explored "Essential Coding Theory" (PDF), clarifying "coding" as error-correcting codes within information theory. It linked these concepts to data compression and AI, and offered supplementary learning resources. #CodingTheory 1/6
Novel construction methods yield quantum error-correcting codes with improved parameters using hulls and sums of separable constacyclic codes over mixed alphabets, demonstrating superior code rates and minimum distances.
#QuantumErrorCorrection #CodingTheory #Research
#QuantumErrorCorrection #CodingTheory #Research
Quantum Error-Correcting Codes from Separable Constacyclic Codes
arxiv.org
June 23, 2026 at 1:48 PM
Novel construction methods yield quantum error-correcting codes with improved parameters using hulls and sums of separable constacyclic codes over mixed alphabets, demonstrating superior code rates and minimum distances.
#QuantumErrorCorrection #CodingTheory #Research
#QuantumErrorCorrection #CodingTheory #Research
Researchers developed a geometric framework revealing that linearized Reed-Solomon codes satisfy surprising structural constraints—potentially enabling more efficient post-quantum cryptographic systems and network coding applications.
#PostQuantumCryptography #CodingTheory #News
#PostQuantumCryptography #CodingTheory #News
Q-Analogue Framework Reveals Structural Properties of Linearized Reed-Solomon Codes for Cryptography
quantumzeitgeist.com
June 22, 2026 at 1:45 PM
Researchers developed a geometric framework revealing that linearized Reed-Solomon codes satisfy surprising structural constraints—potentially enabling more efficient post-quantum cryptographic systems and network coding applications.
#PostQuantumCryptography #CodingTheory #News
#PostQuantumCryptography #CodingTheory #News
Comprehensive analysis of almost maximum distance separable (AMDS) constacyclic codes and quantum AMDS codes using CSS construction framework for enhanced quantum error correction capabilities in finite field applications.
#QuantumErrorCorrection #CodingTheory #Research
#QuantumErrorCorrection #CodingTheory #Research
AMDS and Quantum AMDS Constacyclic Codes of Length 4pς over Finite Fields
arxiv.org
May 25, 2026 at 2:34 PM
Comprehensive analysis of almost maximum distance separable (AMDS) constacyclic codes and quantum AMDS codes using CSS construction framework for enhanced quantum error correction capabilities in finite field applications.
#QuantumErrorCorrection #CodingTheory #Research
#QuantumErrorCorrection #CodingTheory #Research
Characterizes optimal minimum distance of linear codes under parity-check sparsity constraints, with implications for quantum error correction and fault-tolerant systems. Proves Reed-Solomon codes cannot always achieve these theoretical bounds.
#QuantumErrorCorrection #CodingTheory #Research
#QuantumErrorCorrection #CodingTheory #Research
Codes with Support-Constrained Parity Checks
arxiv.org
May 12, 2026 at 8:26 AM
Characterizes optimal minimum distance of linear codes under parity-check sparsity constraints, with implications for quantum error correction and fault-tolerant systems. Proves Reed-Solomon codes cannot always achieve these theoretical bounds.
#QuantumErrorCorrection #CodingTheory #Research
#QuantumErrorCorrection #CodingTheory #Research
New infinite families of λ-constacyclic codes over finite fields with complete parameter characterization, enabling construction of maximal entanglement quantum error-correcting codes and optimal locally recoverable codes.
#CodingTheory #QuantumErrorCorrection #Research
#CodingTheory #QuantumErrorCorrection #Research
Infinite Families of Constacyclic Codes Supporting 3-Designs with Applications to Quantum Error Correction
arxiv.org
May 8, 2026 at 4:50 PM
New infinite families of λ-constacyclic codes over finite fields with complete parameter characterization, enabling construction of maximal entanglement quantum error-correcting codes and optimal locally recoverable codes.
#CodingTheory #QuantumErrorCorrection #Research
#CodingTheory #QuantumErrorCorrection #Research
Gram matrix framework determines hull dimensions of linearized polynomial codes, directly controlling entangled-pair requirements for entanglement-assisted quantum error correction.
#QuantumErrorCorrection #CodingTheory #Research
#QuantumErrorCorrection #CodingTheory #Research
Hull Dimension of Linearized Polynomial Codes via Gram Matrices with Quantum Error Correction Applications
iq.fp2.dev
April 28, 2026 at 9:54 AM
Gram matrix framework determines hull dimensions of linearized polynomial codes, directly controlling entangled-pair requirements for entanglement-assisted quantum error correction.
#QuantumErrorCorrection #CodingTheory #Research
#QuantumErrorCorrection #CodingTheory #Research
New GRL framework yields explicit NMDS criteria, 4 Hermitian self-orthogonal code families, and 4 quantum code families—two infinite quantum NMDS families achieve the quantum Singleton bound minus one, producing new/improved QECCs.
#QuantumErrorCorrection #CodingTheory #Research
#QuantumErrorCorrection #CodingTheory #Research
Generalized Roth-Lempel Codes: NMDS Criteria, Hermitian Self-Orthogonality & Quantum Constructions
iq.fp2.dev
April 14, 2026 at 3:40 AM
New GRL framework yields explicit NMDS criteria, 4 Hermitian self-orthogonal code families, and 4 quantum code families—two infinite quantum NMDS families achieve the quantum Singleton bound minus one, producing new/improved QECCs.
#QuantumErrorCorrection #CodingTheory #Research
#QuantumErrorCorrection #CodingTheory #Research
Upcoming in @SageMath 9.4: Algebraic Geometry (AG) codes, powered by global function fields machinery
https://wiki.sagemath.org/ReleaseTours/sage-9.4#Coding_theory
#Python #CodingTheory #OpenSource
https://wiki.sagemath.org/ReleaseTours/sage-9.4#Coding_theory
#Python #CodingTheory #OpenSource
ReleaseTours/sage-9.4 - Sagemath Wiki
wiki.sagemath.org
December 2, 2024 at 5:34 PM
Upcoming in @SageMath 9.4: Algebraic Geometry (AG) codes, powered by global function fields machinery
https://wiki.sagemath.org/ReleaseTours/sage-9.4#Coding_theory
#Python #CodingTheory #OpenSource
https://wiki.sagemath.org/ReleaseTours/sage-9.4#Coding_theory
#Python #CodingTheory #OpenSource
The authors identify primitive idempotents generating these codes and compute minimum Hamming distances (t = 2), extending previous work by Rakphon et al.
Read more: doi.org/10.1142/S179...
#CodingTheory #FiniteFields #ConstacyclicCodes #HammingDistance
Read more: doi.org/10.1142/S179...
#CodingTheory #FiniteFields #ConstacyclicCodes #HammingDistance
June 10, 2026 at 6:48 AM
The authors identify primitive idempotents generating these codes and compute minimum Hamming distances (t = 2), extending previous work by Rakphon et al.
Read more: doi.org/10.1142/S179...
#CodingTheory #FiniteFields #ConstacyclicCodes #HammingDistance
Read more: doi.org/10.1142/S179...
#CodingTheory #FiniteFields #ConstacyclicCodes #HammingDistance
The authors study a type of code over R = Z₂ + uZ₂ + u²Z₂ (u³ = 0). They look at different ways to measure code weights—like Hamming and Lee—and show how these relate to the code’s dual using MacWilliams identities: doi.org/10.1142/S179...
#CodingTheory #LinearCodes
#CodingTheory #LinearCodes
June 10, 2026 at 5:23 AM
The authors study a type of code over R = Z₂ + uZ₂ + u²Z₂ (u³ = 0). They look at different ways to measure code weights—like Hamming and Lee—and show how these relate to the code’s dual using MacWilliams identities: doi.org/10.1142/S179...
#CodingTheory #LinearCodes
#CodingTheory #LinearCodes
The authors compare two constructions over F₂ (Chang & Hyun vs Wu & Lee), explore their relationships, and derive self-orthogonal codes with generalized Hamming weights: doi.org/10.1142/S179...
#CodingTheory #LinearCodes
#CodingTheory #LinearCodes
June 10, 2026 at 3:44 AM
The authors compare two constructions over F₂ (Chang & Hyun vs Wu & Lee), explore their relationships, and derive self-orthogonal codes with generalized Hamming weights: doi.org/10.1142/S179...
#CodingTheory #LinearCodes
#CodingTheory #LinearCodes
How can graph theory support secure coding?
This paper explores edge-difference total labeling and coloring in bipartite graphs, with applications to graph lattice-based topological coding and computational security: doi.org/10.1142/S179...
#GraphTheory #DiscreteMath #CodingTheory
This paper explores edge-difference total labeling and coloring in bipartite graphs, with applications to graph lattice-based topological coding and computational security: doi.org/10.1142/S179...
#GraphTheory #DiscreteMath #CodingTheory
May 20, 2026 at 11:47 PM
How can graph theory support secure coding?
This paper explores edge-difference total labeling and coloring in bipartite graphs, with applications to graph lattice-based topological coding and computational security: doi.org/10.1142/S179...
#GraphTheory #DiscreteMath #CodingTheory
This paper explores edge-difference total labeling and coloring in bipartite graphs, with applications to graph lattice-based topological coding and computational security: doi.org/10.1142/S179...
#GraphTheory #DiscreteMath #CodingTheory