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[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]-linear codes
- Source :
- IEEE Transactions on Information Theory. Sept, 2002, Vol. 48 Issue 9, p2592, 14 p.
- Publication Year :
- 2002
-
Abstract
- We characterize codes over [Z.sub.p] which are the Gray images of (1 - [p.sup.k])-cyclic codes or cyclic codes over [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (k [greater than or equal to] 1). A necessary and sufficient condition for the Gray image of a [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]-linear (1 - p)-cyclic code to be linear is given. In many cases, this yields an explicit description of the Gray image of a linear (1 - p)-cyclic code over [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], of length relatively prime to p. Linear cyclic codes over [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] a whose Gray images are linear cyclic codes over [Z.sub.p] have been characterized. Some generalizations of these results to the case of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], where k [greater than or equal to] 2, are also obtained. Index Terms--Constacyclic code, cyclic code, Gray map, linear code, quasi-cyclic code.
- Subjects :
- Information theory -- Models
Codes -- Analysis
Subjects
Details
- ISSN :
- 00189448
- Volume :
- 48
- Issue :
- 9
- Database :
- Gale General OneFile
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- edsgcl.91398783