A Generalized Parity Function and Its Use in the Construction of Perfect Codes

DOI10.1137/0607013zbMath0585.94015OpenAlexW1966494597MaRDI QIDQ3712238

Michel Mollard

Publication date: 1986

Published in: SIAM Journal on Algebraic Discrete Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0607013

zbMATH Keywords

product constructionsingle-error-correcting perfect codes

Mathematics Subject Classification ID

Combinatorial codes (94B25) Combinatorial aspects of packing and covering (05B40)

Related Items (16)

On the symmetry group of the Mollard code ⋮ Perfect codes in Doob graphs ⋮ The superstar packing problem ⋮ On non-full-rank perfect codes over finite fields ⋮ Mollard code as a robust nonlinear code ⋮ On \(\mathbb Z_{4}\)-linear codes with the parameters of Reed-Muller codes ⋮ Coordinate transitivity of a class of extended perfect codes and their SQS ⋮ On the construction of transitive codes ⋮ Transitive nonpropelinear perfect codes ⋮ On the Mollard code as a partially robust code ⋮ On perfect binary codes ⋮ Packing in honeycomb networks ⋮ A concatenation construction for propelinear perfect codes from regular subgroups of \(\mathrm{GA}(r,2)\) ⋮ On transitive partitions of an \(n\)-cube into codes ⋮ Full rank perfect codes and \(\alpha \)-kernels ⋮ On transitive uniform partitions of \(F^n\) into binary Hamming codes

Cites Work

• Unnamed Item
• A product construction for perfect codes over arbitrary alphabets (Corresp.)
• A General Product Construction for Error Correcting Codes
• A Combinatorial Construction of Perfect Codes
• Error Detecting and Error Correcting Codes
• On linear and nonlinear single-error-correcting q-nary perfect codes

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