Dual of Codes over Finite Quotients of Polynomial Rings

Nikseresht, Ashkan

doi:10.1016/j.ffa.2017.01.003

arXiv 2016-05-11 DOI 10.1016/j.ffa.2017.01.003 0 views

Dual of Codes over Finite Quotients of Polynomial Rings

Nikseresht, Ashkan

Information Theory Rings and Algebras 94B05, 11T71, 11T06 E.4

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Let A=F[x]/ f(x), where f(x) is a monic polynomial over a finite field F. In this paper, we study the relation between A-codes and their duals. In particular, we state a counterexample and a correction to a theorem of Berger and El Amrani (Codes over finite quotients of polynomial rings, Finite Fields Appl. 25 (2014), 165--181) and present an efficient algorithm to find a system of generators for the dual of a given A-code. Also we characterize self-dual A-codes of length 2 and investigate when the F-dual of A-codes are A-codes.

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