AI & ML
Euclidean Hulls of Double Cyclic Codes of Arbitrary Block Lengths
arXiv math.IT0 views
arXiv:2611.13481v1 Announce Type: new Abstract: 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.
Source：https://arxiv.org/abs/2611.13481PreviousMinimum Synthesis Time for Single-Deletion Correcting Codes of Prescribed SizeNextThird-Order Asymptotics for Fixed-Length Lossy Compression of Discrete Memoryless Sources
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