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Bijective Equivalence Mapping from F2[D2n]-Code to F2[C2n]-Code for Integer  n=3,4,5…,n


NK Agrawal, Dhananjay Kumar Mishra, Ram Naresh Das
Pages: 113-128
ISBN: 978-93-5834-983-2


Recent Research Trends in Mathematics (Volume -7)

Recent Research Trends in Mathematics
(Volume - 7)

Abstract

A group ring code is a kind of code which is made up of group ring structure. Every group ring code over a dihedral group for given sub-module becomes equivalent to some of group ring code over cyclic group for a given suitable other sub-module for integer n=3, 4, 5, …, n. But an F2[C4]-code cannot be an F2[D4]-code. Every cyclic code has spanning set. Due to this reason every dihedral group ring code is equivalent to some of cyclic group ring code up to adjustable permutations. Thus it is a bijective equivalent mapping, this means there a bijective mapping from F2[D2n]-codes to F2[C2n]-code. If fu be the require mapping, and hence fu(C_(D_2n ) (z,N)) → C_(C_2n ) (z,M) for n=3,4,5,….,n. Such type of coding concept is utilized in communication areas to transmit information and to maintain secrecy.

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