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|Title:||An explicit expression for Euclidean self-dual cyclic codes over F<inf>2<sup>m</sup></inf>+uF<inf>2<sup>m</sup></inf> of length 2<sup>s</sup>|
Hai Q. Dinh
Hai Q. Dinh
|Abstract:||Let F2m be the finite field of 2m elements and s be any positive integer. The existing literature only gives an effective calculation method to represent all distinct Euclidean self-dual cyclic codes of length 2s over the finite chain ring F2m+uF2m(u2=0), such as in Cao et al., (2019). As a development of this topic, we provide an explicit expression for each of these self-dual cyclic codes, using binomial coefficients. The Gray image of any self-dual cyclic code over F2m+uF2m of length 2s is a self-dual 2-quasi-cyclic code over F2m of length 2s+1. In particular, we give a generator matrix for each of these self-dual 2-quasi-cyclic codes over F2m.|
|Appears in Collections:||CMUL: Journal Articles|
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