The hulls of linear and cyclic codes have been extensively studied due to their wide applications. The dimensions and average dimension of the Euclidean hull of linear and cyclic codes have been well-studied. In this paper, the average dimension of the Hermitian hull of constacyclic codes of length n over a finite field Fq2 is determined together with some upper and lower bounds. It turns out t...

We study (1 + 2v)-constacyclic codes over R + vR and their Gray images, where v + v = 0 and R is a finite chain ring with maximal ideal  and nilpotency index e. It is proved that the Gray map images of a (1 + 2v)-constacyclic codes of length n over R + vR are distance-invariant linear cyclic codes of length 2n over R. The generator polynomials of this kind of codes for length n are determined,...

As a generalization of BCH codes, constacyclic codes have become good source for constructing optimal codes. However, the parameters these are not easy to determine in general. In this paper, we investigate class $ q $-ary with length \frac{q^{m}+1}{2} and compute their exact dimensions some ranges designed distance. particular, study distance larger range than known results.

Linear codes may be endowed with cyclic structures by means of skew polynomial rings. This is the case of Piret cyclic convolutional codes [26] and the subsequent generalizations and alternatives (see [27], [14], [11], [25], [16], [20]). Non commutative cyclic structures of this kind have been also considered for block linear codes ([7], [5], [4], [12], [1]), and for linear codes over commutati...

In this paper, we study the algebraic structure of Z2[u]Z2[u, v]-additive codes which are Z2[u, v]-submodules where u 2 = v2 = 0 and uv = vu. In particular, we determine a Gray map from Z2[u]Z2[u, v] to Z 2α+8β 2 and study generator and parity check matrices for these codes. Further we study the structure of Z2[u]Z2[u, v]additive cyclic codes and constacyclic codes.

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

The symbol-pair codes over finite fields have been raised for symbol-pair read channels and motivated by application of high-density data storage technologies [1, 2]. Their generalization is the code for b-symbol read channels (b > 2). Many MDS codes for b-symbol read channels have been constructed which meet the Singleton-like bound ([3, 4, 10] for b = 2 and [11] for b > 2). In this paper we s...