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Sharp p-Divisibility of Weights in Abelian Codes Over Z/pdZ.
- Source :
-
IEEE Transactions on Information Theory . Dec2008, Vol. 54 Issue 12, p5354-5380. 27p. - Publication Year :
- 2008
-
Abstract
- A theorem of McEliece on the p-divisibility of Hamming weights in cyclic codes over Fp is generalized to Abelian codes over Z/pd Z. This work improves upon results of Helleseth—Kumar—Moreno—Shanbhag, Calderbank—Li—Poonen, Wilson, and Katz. These previous attempts are not sharp in general, i.e., do not report the full extent of the p-divisibility except in special cases, nor do they give accounts of the precise circumstances under which they do provide best possible results. This paper provides sharp results on p-divisibilities of Hamming weights and counts of any particular symbol for an arbitrary Abelian code over Z/pd Z. It also presents sharp results on 2-divisibilities of Lee and Euclidean weights for Abelian codes over Z/4Z. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 54
- Issue :
- 12
- Database :
- Academic Search Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 35843429
- Full Text :
- https://doi.org/10.1109/TIT.2008.2006434