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In this paper, we give the structures of all ( 1 + u + v ) -constacyclic codes of length 2 s over F 2 + u F 2 + v F 2 + u v F 2 , we also obtain the number of codewords, and the dual of each constacyclic code. Among other results, we study the form of such constacyclic codes that are self-dual and give the number of these codes. We end by giving all self-dual constacyclic codes of length 2, 4 and 8. [ABSTRACT FROM AUTHOR]

In this paper, we describe the Chinese Remainder Theorem for studying Abelian codes of length $$N$$ over the ring $${\mathbb {Z}}_{m}$$ , where $$m=\prod _{i=1}^{s}p_{i}, $$ $$k=\prod _{i=1}^{s}p_{i}^{t_{i}}, \, N=kn, \, p_{i}$$ are distinct primes, $$s$$ is a positive integer, $$t_{i}$$ are positive integers and $$n$$ is a positive integer prime to $$k.$$ The structure theorems for Abelian codes and their duals in $${\mathbb {Z}}_{m}G$$ are obtained, where $$G=C_{k} \times H,$$ $$C_{k}$$ denotes the cyclic group of order $$k$$ and $$H$$ denotes a group of order $$n.$$ The existence of self-orthogonal and the nonexistence of self-dual Abelian codes over $${\mathbb {Z}}_{m}$$ are studied. [ABSTRACT FROM AUTHOR]

The transform domain characterization of cyclic codes over finite fields using Discrete Fourier Transform(DFT) over an appropriate extension field is well known. In this paper, we extend this transform domain characterization for cyclic codes over F p + uF p + ··· + u k-1 F p . We give a way to characterize cyclic codes over F p + uF p + ··· + u k-1 F p by Mattson-Solomon polynomials and multiple defining sets. [ABSTRACT FROM AUTHOR]