An explicit expression for Euclidean self-dual cyclic codes over \(\mathbb{F}_{2^m} + u \mathbb{F}_{2^m}\) of length \(2^s\)

DOI10.1016/j.disc.2021.112323zbMath1472.94095OpenAlexW3127678322WikidataQ114190633 ScholiaQ114190633MaRDI QIDQ2659236

Jirakom Sirisrisakulchai, Yuan Cao, Hai Quang Dinh, Gui Dong Wang, Yong-Lin Cao

Publication date: 25 March 2021

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

Full work available at URL: https://doi.org/10.1016/j.disc.2021.112323

zbMATH Keywords

cyclic codebinomial coefficientquasi-cyclic codeKronecker product of matricesGray imageEuclidean self-dual code

Mathematics Subject Classification ID

Cyclic codes (94B15)

Related Items (1)

An explicit expression for all distinct self-dual cyclic codes of length \(p^k\) over Galois ring \(\mathrm{GR}(p^2,m)\)

Cites Work

• Unnamed Item
• Negacyclic codes of length \(2p^s\) over \(\mathbb{F}_{p^m} + u \mathbb{F}_{p^m}\)
• New extremal binary self-dual codes from \(\mathbb{F}_4 + u \mathbb{F}_4\)-lifts of quadratic circulant codes over \(\mathbb{F}_4\)
• On constacyclic codes of length \(4p^s\) over \(\mathbb{F}_{p^m} +u\mathbb{F}_{p^m}\)
• Constacyclic codes of length \(p^s\) over \(\mathbb F_{p^m} + u\mathbb F_{p^m}\)
• Self-dual codes over commutative Frobenius rings
• Constacyclic codes of length \(2p^{s}\) over \(\mathbb{F}_{p^m} + u \mathbb{F}_{p^m}\)
• Various constructions for self-dual codes over rings and new binary self-dual codes
• On \((1 - u)\)-cyclic codes over \(\mathbb F_{p^k}+u\mathbb F_{p^k}\)
• Applications of coding theory to the construction of modular lattices
• Type II codes over \(\mathbb{F}_{2^m} + u\mathbb{F}_{2^m}\)
• Type II codes over \(\mathbb F_2+ u\mathbb F_2\) and applications to Hermitian modular forms
• Constacyclic codes of length \(np^s\) over \(\mathbb{F}_{p^m}+u\mathbb{F}_{p^m}\)
• Self-dual abelian codes in some nonprincipal ideal group algebras
• An efficient method to construct self-dual cyclic codes of length \(p^s\) over \(\mathbb{F}_{p^m} + u \mathbb{F}_{p^m} \)
• Constacyclic codes over \(\mathbb F_2 + u\mathbb F_2\)
• Construction and enumeration for self-dual cyclic codes of even length over \(\mathbb{F}_{2^m} + u \mathbb{F}_{2^m} \)
• On the decomposition of self-dual codes over \(\mathbb F_2 + u\mathbb F_2\) with an automorphism of odd prime order
• (1 + u) constacyclic and cyclic codes over \(F_{2} + uF_{2}\)
• An explicit representation and enumeration for self-dual cyclic codes over \(\mathbb{F}_{2^m}+u\mathbb{F}_{2^m}\) of length \(2^s\)
• Extremal binary self-dual codes of lengths 64 and 66 from four-circulant constructions over F2+uF2
• CONSTRUCTION OF SELF-DUAL CODES OVER F₂+ uF₂
• The Z/sub 4/-linearity of Kerdock, Preparata, Goethals, and related codes
• Type IV self-dual codes over rings
• Construction of optimal Type IV self-dual codes over F/sub 2/+uF/sub 2/
• Type II codes over F/sub 2/+uF/sub 2/
• Cyclic codes and self-dual codes over F/sub 2/+uF/sub 2/
• Constacyclic Codes of Length $2^s$ Over Galois Extension Rings of ${\BBF}_{2}+u{\BBF}_2$
• Type II codes over \(\mathbb{F}_4+u\mathbb{F}_4\)

This page was built for publication: An explicit expression for Euclidean self-dual cyclic codes over \(\mathbb{F}_{2^m} + u \mathbb{F}_{2^m}\) of length \(2^s\)