FEW-WEIGHT CODES FROM TRACE CODES OVER

DOI10.1017/S0004972718000291zbMath1430.94097OpenAlexW2802825310MaRDI QIDQ4576831

Chenchen Wang, Yue Guan, Minjia Shi, Patrick Solé

Publication date: 11 July 2018

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0004972718000291

zbMATH Keywords

trace codesdefining setfew-weights codesGray may

Mathematics Subject Classification ID

Linear codes (general theory) (94B05) Cyclic codes (94B15) Authentication, digital signatures and secret sharing (94A62)

Related Items (8)

\(G\)-codes, self-dual \(G\)-codes and reversible \(G\)-codes over the ring \(\mathscr{B}_{j,k} \) ⋮ Few-weight codes over a non-chain ring associated with simplicial complexes and their distance optimal gray image ⋮ New classes of binary few weight codes from trace codes over a chain ring ⋮ Linear codes over finite rings are trace codes ⋮ Two classes of few-Lee weight \(\mathbb{Z}_2 [u\)-linear codes using simplicial complexes and minimal codes via Gray map] ⋮ Minimal and optimal binary codes obtained using \(C_D\)-construction over the non-unital ring \(I\) ⋮ Five-weight codes from three-valued correlation of M-sequences ⋮ Few-weight \(\mathbb{Z}_p\mathbb{Z}_p[u\)-additive codes from down-sets]

Cites Work

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• Optimal binary codes from trace codes over a non-chain ring
• Codes over \(R_k\), Gray maps and their binary images
• Weights of linear codes and strongly regular normed spaces
• A Class of Two-Weight and Three-Weight Codes and Their Applications in Secret Sharing
• Design Methods for Maximum Minimum-Distance Error-Correcting Codes
• The Geometry of Two-Weight Codes
• Two New Families of Two-Weight Codes
• Minimal vectors in linear codes

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