The linear programming bound for codes over finite Frobenius rings

DOI10.1007/s10623-006-9035-4zbMath1133.94020OpenAlexW1984973158MaRDI QIDQ2384000

Marcus Greferath, Eimear Byrne, Michael E. O'Sullivan

Publication date: 20 September 2007

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

Full work available at URL: https://doi.org/10.1007/s10623-006-9035-4

zbMATH Keywords

codes over ringsblock codeshomogeneous weightslinear-programming bound

Mathematics Subject Classification ID

Quasi-Frobenius rings (16L60) Bounds on codes (94B65) Theory of error-correcting codes and error-detecting codes (94B99)

Related Items

The homogeneous weight partition and its character-theoretic dual ⋮ On the ℤ_q-Simplex codes and its weight distribution for dimension 2 ⋮ New bounds for codes over finite Frobenius rings ⋮ Duality of codes supported on regular lattices, with an application to enumerative combinatorics ⋮ Partitions of matrix spaces with an application to \(q\)-rook polynomials ⋮ Partitions of Frobenius rings induced by the homogeneous weight ⋮ MacWilliams extension theorems and the local-global property for codes over Frobenius rings ⋮ Several classes of linear codes with a few weights from defining sets over \(\mathbb {F}_p+u\mathbb {F}_p\) ⋮ Fourier-reflexive partitions and MacWilliams identities for additive codes

Uses Software

• Magma
• GLPK

Cites Work

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• A metric for codes over residue class rings
• \(F\)-partitions of cyclic groups
• The Magma algebra system. I: The user language
• On Fourier-invariant partitions of finite Abelian groups and the MacWilliams identity for group codes
• Weighted modules and representations of codes
• Finite-ring combinatorics and MacWilliams' equivalence theorem
• On the optimal \(\mathbb Z_4\) codes of type II and length 16
• On bounds for codes over Frobenius rings under homogeneous weights
• Kerdock code in a cyclic form
• Duality for modules over finite rings and applications to coding theory
• The Z/sub 4/-linearity of Kerdock, Preparata, Goethals, and related codes
• On the isometries between Z(p/sup k/) and Z/sub p//sup k/
• Gray isometries for finite chain rings and a nonlinear ternary (36, 3/sup 12/, 15) code
• A Z/sub 8/-linear lift of the binary Golay code and a nonlinear binary (96,2/sup 37/,24)-code
• Z/sub 2/k-linear codes
• Characterization of finite Frobenius rings