Finite-ring combinatorics and MacWilliams' equivalence theorem
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Publication:1586124
DOI10.1006/jcta.1999.3033zbMath1087.94022OpenAlexW1984488462MaRDI QIDQ1586124
Stefan E. Schmidt, Marcus Greferath
Publication date: 2000
Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)
Full work available at URL: https://semanticscholar.org/paper/6385e9cfc0ff17bdd42f473cec23606796e834ee
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Cites Work
- A metric for codes over residue class rings
- Characters and the equivalence of codes
- Combinatorial theory.
- Kerdock code in a cyclic form
- An elementary proof of the MacWilliams theorem on equivalence of codes
- The Z/sub 4/-linearity of Kerdock, Preparata, Goethals, and related codes
- [https://portal.mardi4nfdi.de/wiki/Publication:5731810 On the foundations of combinatorial theory I. Theory of M�bius Functions]
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