Constacyclic codes over finite fields are a family of linear codes and contain cyclic codes as
a subclass. Constacyclic codes are related to many areas of mathematics and outperform …

Recently, b-symbol codes are proposed to protect against b-symbol errors in b-symbol read
channels. It is an interesting subject of study to consider the complete b-symbol weight …

Let be a simple-root cyclic code and let be the subgroup of the automorphism group of
generated by the cyclic shift of and the scalar multiplications of. In this paper, we find an …

Cyclic codes are an interesting type of linear codes and have wide applications in
communication and storage systems due to their efficient encoding and decoding …

We determine the weight spectra of the Reed-Muller codes RM (m− 3, m) for m≥ 6 and RM
(m− 4, m) for m≥ 8. The technique used is induction on m, using that the sum of two weights …

Let be an arbitrary simple-root cyclic code and let be the subgroup of (the automorphism
group of) generated by the multiplier, the cyclic shift and the scalar multiplications. To the …

For a simple-root λ-constacyclic code C over F q, let< ρ> and< ρ, M> be the subgroups of the
automorphism group of C generated by the cyclic shift ρ, and by the cyclic shift ρ and the …

In the recent work\cite {shi18}, a combinatorial problem concerning linear codes over a finite
field $\F_q $ was introduced. In that work the authors studied the weight set of an $[n, k] _q …

The number of nonzero weights of a linear code is essential in coding theory as it unveils
salient properties of the code, such as its covering radius. In this paper, we establish two …

A linear $[n, k] _q $ code $ C $ is said to be a full weight spectrum (FWS) code if there exist
codewords of each nonzero weight less than or equal to $ n $. In this brief communication …