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Generalized Gray map and a class of p-ary nonlinear codes.
- Source :
-
Finite Fields & Their Applications . Nov2015, Vol. 36, p81-97. 17p. - Publication Year :
- 2015
-
Abstract
- In this paper, we investigate a generalized Gray map G on Z p k with p a prime, which generalizes a Carlet's result in [1] . For a Z p k -valued function f ( x ) , we use exponential sums to express the Hamming weight of G ( f ( x ) ) . As an application, a family of nonlinear codes over F p is obtained from the generalized Gray map. We use the Weil-type exponential sums over Galois rings to provide a lower bound for the minimum distance of these codes. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10715797
- Volume :
- 36
- Database :
- Academic Search Index
- Journal :
- Finite Fields & Their Applications
- Publication Type :
- Academic Journal
- Accession number :
- 109495936
- Full Text :
- https://doi.org/10.1016/j.ffa.2015.06.006