For any given positive integer m, a necessary and sufficient condition for the existence of TypeI madic constacyclic codes is given. Furthermore, for any given integer s, a necessary and sufficient condition for s to be a multiplier of a TypeI polyadic constacyclic code is given. As an application, some optimal codes from TypeI polyadic constacyclic codes, including generalized ReedSolomon codes and alternant maximum distance separable codes, are constructed.

A Note on Isodual Constacyclic Codes09/01/2014This note gives a counterexample of Theorem 20 in the paper of Blackford (2013) [2]. The counterexample shows that [2, Theorem 20] is incorrect. Furthermore, we provide corrections to the above result. 
Constacyclic codes of length 2ps over F p m + u F p m01/01/2016The aim of this paper is to determine the algebraic structures of all λconstacyclic codes of length 2 p s over the finite commutative chain ring F p m + u F p m , where p is an odd prime and u 2 = 0 . For this purpose, the situation of λ is mainly divided into two cases separately. If the unit λ is not a square and λ = α + u β for nonzero elements α , β of F p m , it is shown that the ambient ring ( F p m + u F p m ) x / { x 2 p s  ( α + u β ) } is a chain ring with the unique maximal ideal { x 2  α 0 } , and thus ( α + u β ) constacyclic codes are { ( x 2  α 0 ) i } for 0 ≤ i ≤ 2 p s . If the unit λ is not a square and λ = γ for some nonzero element γ of F p m , such λconstacyclic codes are classified into 4 distinct types of ideals. The detailed structures of ideals in each type are provided. Among other results, the number of codewords and the dual of every λconstacyclic code are obtained. 
RepeatedRoot Constacyclic Codes of Length 2ℓmpn05/01/2015For any different odd primes ℓ and p, structure of constacyclic codes of length 2ℓmpn over the finite field Fq of characteristic p and their duals is established in terms of their generator polynomials. Among other results, the characterization and enumeration of all linear complementary dual and selfdual constacyclic codes of length 2ℓmpn are obtained. 
RepeatedRoot Constacyclic Codes of Length ℓp^s and Their Duals11/20/2014An equivalence relation is introduced on the nonzero elements of the finite field Fpm to classify constacyclic codes of arbitrary length over Fpm. According to the equivalence classes, all constacyclic codes of length ℓps over Fpm and their duals are characterized, where ℓ is a prime different from p and s is a positive integer. Selfdual cyclic codes of length ℓps over Fpm exist precisely when p is equal to two; in this case, all selfdual cyclic codes of length 2sℓ over F2m are presented. 
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