On matrix-product structure of repeated-root constacyclic codes over finite fields

Abstract

For any prime number p, positive integers m, k, n satisfying gcd(p, n) = 1 and λ 0 ∈ F × p m , we prove that any λ p k 0 -constacyclic code of length p k n over the finite field F p m is monomially equivalent to a matrix-product code of a nested sequence of p k λ 0 -constacyclic codes with length n over F p m .

Quantum Codes Obtained From Constacyclic Codes Over a Family of Finite Rings Fp[u₁, u₂, …, us]

“…x n −λ we can say, a linear code C is a λ-constacyclic code of length n over R s if and only if it is an ideal of the ring R s [x]/ x n −λ . Constacyclic codes over finite fields and finite commutative Frobenious rings have been studied extensively by many authors (see, e.g., [12], [13], [14], [15], [16], [17], [18], [19], [20], [31].)…”

Constacyclic codes of length $ 8p^s $ over $ \mathbb F_{p^m} + u\mathbb F_{p^m} $

“…In 2018, we established successfully all negacyclic codes of length 4p s over F p m + uF p m [32]. After that, some authors extended these problems to many more general lengths and alphabets (see, e.g., [11], [12], [13], [14], [15], [16], [17], [18], [19], [39], [50]).…”

MDS Constacyclic Codes and MDS Symbol-Pair Constacyclic Codes

“…In a recent work, Dinh [25] classified and gave the detailed structures of all constacyclic codes of length p s over R; and in 2012 [24], Dinh provided that for all constacyclic codes of length 2p s over R. In 2018, we established successfully all negacyclic and constacyclic codes of length 4p s over R [31], [33], [34], [35]. After that, some authors extended these problems to many more general lengths and alphabets (see, e.g., [6], [7], [8], [9], [10], [11], [12], [13], [14], [32]).…”