On the distances of cyclic codes of length \(2^e\) over \(\mathbb Z_4\)

DOI10.1016/j.disc.2009.07.018zbMath1182.94058OpenAlexW1983483270MaRDI QIDQ1045137

Shixin Zhu, Xiaoshan Kai

Publication date: 15 December 2009

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.disc.2009.07.018

zbMATH Keywords

Hamming distancescyclic codescodes over ringsLee distancesquaterny codes

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Cyclic codes (94B15)

Related Items (13)

Repeated-root constacyclic codes of length \(n l p^s\) ⋮ A mass formula for cyclic codes over Galois rings of characteristic \(p^3\) ⋮ Repeated-root constacyclic codes of length \(3lp^s\) and their dual codes ⋮ Lee weights of cyclic self-dual codes over Galois rings of characteristic \(p^2\) ⋮ Repeated-root constacyclic codes of length \(3 \ell^m p^s\) ⋮ Lee distance of cyclic and \((1 + u\gamma)\)-constacyclic codes of length \(2^s\) over \(\mathbb{F}_{2^m} + u \mathbb{F}_{2^m} \) ⋮ Repeated-root constacyclic codes of length \(2 \ell^m p^n\) ⋮ Repeated-root constacyclic codes of length \(6lp^s\) ⋮ The minimum Hamming distances of repeated-root cyclic codes of length \(6p^s\) and their MDS codes ⋮ Repeated-root constacyclic codes of length \(k\ell p^s\) ⋮ The Hamming distances of repeated-root cyclic codes of length \(5 p^s\) ⋮ On the construction of self-dual cyclic codes over \(\mathbb{Z}_4\) with arbitrary even length ⋮ Lee distance distribution of repeated-root constacyclic codes over \(\mathrm{GR}(2^e,m)\) and related MDS codes

Cites Work

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• Cyclic codes over the integers modulo \(p^m\).
• Cyclic codes over finite rings
• Cyclic codes over \(\mathbb{Z}_{4}\) of oddly even length.
• Modular and \(p\)-adic cyclic codes
• Cyclic codes over \(\mathbb Z_4\) of even length
• On the generators of Z/sub 4/ cyclic codes of length 2/sup e/
• Complete Distances of All Negacyclic Codes of Length $2^{s}$ Over $\BBZ _{2^{a}}$
• Codes over integer residue rings
• Lee metric codes over integer residue rings (Corresp.)
• The Z/sub 4/-linearity of Kerdock, Preparata, Goethals, and related codes
• On the Hamming distance of linear codes over a finite chain ring
• Cyclic codes and quadratic residue codes over Z/sub 4/
• Codes over certain rings

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