A group ring construction of the \([48,24,12]\) Type II linear block code

DOI10.1007/s10623-011-9530-0zbMath1235.94060OpenAlexW1995108997MaRDI QIDQ664388

Ian Vince McLoughlin

Publication date: 1 March 2012

Published in: Designs, Codes and Cryptography (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10623-011-9530-0

zbMATH Keywords

self-dual codeserror correcting codesType II codesgroup ringlinear block code

Mathematics Subject Classification ID

Linear codes (general theory) (94B05) Group rings of finite groups and their modules (group-theoretic aspects) (20C05) Other types of codes (94B60) Algebraic systems of matrices (15A30)

Related Items (14)

Concatenated structure of left dihedral codes ⋮ Group rings, \(G\)-codes and constructions of self-dual and formally self-dual codes ⋮ Construction and enumeration of left dihedral codes satisfying certain duality properties ⋮ Quadruple bordered constructions of self-dual codes from group rings ⋮ Bordered constructions of self-dual codes from group rings and new extremal binary self-dual codes ⋮ Double bordered constructions of self-dual codes from group rings over Frobenius rings ⋮ Unnamed Item ⋮ Left dihedral codes over Galois rings \(\mathrm{GR}(p^2, m)\) ⋮ Constructions for self-dual codes induced from group rings ⋮ \(2^n\) bordered constructions of self-dual codes from group rings ⋮ Left dihedral codes over finite chain rings ⋮ An altered four circulant construction for self-dual codes from group rings and new extremal binary self-dual codes. I ⋮ Hermitian duality of left dihedral codes over finite fields ⋮ A modified bordered construction for self-dual codes from group rings

Uses Software

• GAP

Cites Work

• Unnamed Item
• Unnamed Item
• Codes from zero-divisors and units in group rings
• A Group Ring Construction of the Extended Binary Golay Code
• A Prize Problem in Coding Theory
• Fundamentals of Error-Correcting Codes
• The extended quadratic residue code is the only (48,24,12) self-dual doubly-even code
• Some Sphere Packings in Higher Space
• Is there a (72,36) d = 16 self-dual code? (Corresp.)

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