Let SLAut (F qn) denote the group of all semilinear isometries on F qn, where q= pe is a
prime power. In this paper, we investigate some general properties of linear codes …

By using linear algebra over finite commutative rings, we will present some judging
criterions for linear complementary dual (LCD) codes over rings, in particular, free LCD …

Matrix-product (MP) codes are a type of long codes formed by combining several
commensurate constituent codes with a defining matrix. In this paper, we study the MP code …

For any prime number p, positive integers m, k, n, where n satisfies gcd (p, n)= 1, and for any
non-zero element λ 0 of the finite field F pm of cardinality pm, we prove that any λ 0 p k …

Abstract In 2001, Blackmore and Norton introduced an important tool called matrix-product
codes, which turn out to be very useful to construct new quantum codes of large lengths. To …

Let $\mathrm {SLAut}(\mathbb {F} _ {q}^{n}) $ denote the group of all semilinear isometries
on $\mathbb {F} _ {q}^{n} $, where $ q= p^{e} $ is a prime power. In this paper, we …

This paper provides the Generalized Mattson Solomon polynomial for repeated-root
polycyclic codes over local rings that gives an explicit decomposition of them in terms of …

A well‐known lower bound (over finite fields and some special finite commutative rings) on
the Hamming distance of a matrix‐product code (MPC) is shown to remain valid over any …

In this paper, a necessary and sufficient condition for the homogeneous distance on an
arbitrary finite commutative principal ideal ring to be a metric is obtained. We completely …

The matrix-product (MP) code $\mathcal {C} _ {A, k}:=[\mathcal {C} _ {1},\mathcal {C} _
{2},\ldots,\mathcal {C} _ {k}]\cdot A $ with a non-singular by column (NSC) matrix $ A $ plays …