For units δ and α in Fpm, the structure of (δ + αu 2)-constacyclic codes of length p over Fpm + uFpm + u 2 Fpm is studied and self-dual (δ + αu 2)constacyclic codes are analyzed.

Let p be an odd prime, s,m be positive integers and Fpm be the finite field with p m elements. In this paper, we determine all constacyclic codes of length 4p over the finite commutative chain ring R = Fpm + uFpm with unity, where u 2 = 0. We also determine their dual codes and list some isodual constacyclic codes of length 4p over R.

We give the structure of λ-constacyclic codes of length pm over R = Fpr +uFpr + . . .+uFpr with λ ∈ F ∗ pr . We also give the structure of λ-constacyclic codes of length pm with λ = α1 + uα2 + . . .+ u αe−1, where α1, α2 6= 0 and study the self-duality of these codes.

Cyclic, negacyclic and constacyclic codes are part of a larger class of codes called polycyclic codes; namely, those codes which can be viewed as ideals of a factor ring of a polynomial ring. The structure of the ambient ring of polycyclic codes over GR(p,m) and generating sets for its ideals are considered. It is shown that these generating sets are strong Groebner bases. A method for finding ...

We introduce a Gray map from F2m + uF2m to F 2m 2 and study (1 + u)-constacyclic codes over F2m + uF2m ,where u 2 = 0. It is proved that the image of a (1+u)-constacyclic code length n overF2m+uF2m under the Gray map is a distance-invariant quasi-cyclic code of indexm and length 2mn over F2. We also prove that every code of length 2mnwhich is the Gray image of cyclic codes overF2m+uF2m of lengt...

We first define a new Gray map from R = Z4+uZ4 to Z 2 4, where u 2 = 1 and study (1 + 2u)-constacyclic codes over R. Also of interest are some properties of (1 + 2u)constacyclic codes over R. Considering their Z4 images, we prove that the Gray images of (1+2u)-constacyclic codes of length n over R are cyclic codes of length 2n over Z4. In many cases the latter codes have better parameters than ...

For any different odd primes l and p, structure of constacyclic codes of length 2lp over a finite field Fq of characteritic p and their duals is established in term of their generator polynomials. Among other results, all linear complimentary dual and self-dual constacyclic codes of length 2lp over Fq are obtained.

In this paper we introduce the notion of λ-constacyclic codes over finite rings R for arbitrary element λ R. We study non-invertible-element constacyclic (NIE-constacyclic codes) principal ideal (PIRs). determine algebraic structures all NIE-constacyclic chain rings, give unique form sets defining polynomials and obtain their minimum Hamming distances. A general duals is also provided. particul...