Optimal non-projective linear codes constructed from down-sets

DOI10.1016/j.dam.2018.07.007zbMath1431.94153OpenAlexW2887962334MaRDI QIDQ1720320

Jong Yoon Hyun, Minwon Na, Hyun Kwang Kim

Publication date: 8 February 2019

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

Full work available at URL: https://doi.org/10.1016/j.dam.2018.07.007

zbMATH Keywords

weight distributionoptimal linear codesdown-setsminimal linear codesrelative two-weight linear codes

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Linear codes (general theory) (94B05) Authentication, digital signatures and secret sharing (94A62)

Related Items (9)

Few-weight codes over a non-chain ring associated with simplicial complexes and their distance optimal gray image ⋮ Two classes of optimal \(p\)-ary few-weight codes from down-sets ⋮ New classes of binary few weight codes from trace codes over a chain ring ⋮ Several classes of linear codes with few weights over finite fields ⋮ Three new constructions of optimal linear codes with few weights ⋮ Few-weight codes over \(\mathbb{F}_p + u \mathbb{F}_p\) associated with down sets and their distance optimal Gray image ⋮ Octanary linear codes using simplicial complexes ⋮ A unified construction of optimal and distance optimal two or three-weight codes ⋮ Few-weight \(\mathbb{Z}_p\mathbb{Z}_p[u\)-additive codes from down-sets]

Uses Software

• Code Tables

Cites Work

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• On relative constant-weight codes
• On Minimal and Quasi-minimal Linear Codes
• Face Numbers of Down-Sets
• Minimal vectors in linear codes
• Algebraically punctured cyclic codes
• A Bound for Error-Correcting Codes

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