← 研踪 PaperTrailarXiv:2611.13481 · v1
Euclidean Hulls of Double Cyclic Codes of Arbitrary Block Lengths
首次提交 2026-11-10 10:43
版本更新 2026-11-10 10:43
雷达观测 2026-11-11 11:04
摘要
Gao et al. \cite{GWF23} recently explored the Euclidean hulls of double cyclic codes over $\mathbb{Z}_2$. While they found answers for non-separable codes with coprime lengths ($\gcd(r, s) = 1$), the non-coprime case ($\gcd(r, s) > 1$) remained an open question. This paper completely solves that problem for all possible block lengths. We calculate the exact generator polynomials for the hull and show the precise conditions needed for a non-separable code to turn into a separable one. Using this, we show how to construct non-separable LCD codes. We also include several numerical examples to confirm our findings.
观测到的版本
相邻记录可能跳过中间版本；首次发现 v2 及以上也会标为版本更新。
v1 · 2026-11-10 10:43 · 最新观测版本
Euclidean Hulls of Double Cyclic Codes of Arbitrary Block Lengths
Gao et al. \cite{GWF23} recently explored the Euclidean hulls of double cyclic codes over $\mathbb{Z}_2$. While they found answers for non-separable codes with coprime lengths ($\gcd(r, s) = 1$), the non-coprime case ($\gcd(r, s) > 1$) remained an open question. This paper completely solves that problem for all possible block lengths. We calculate the exact generator polynomials for the hull and show the precise conditions needed for a non-separable code to turn into a separable one. Using this, we show how to construct non-separable LCD codes. We also include several numerical examples to confirm our findings.
查看此版本解读 →查看此版本原文 ↗