Polycyclic codes are a generalization of cyclic and constacyclic codes. Even though they have been known since 1972 received some attention more recently, there not many studies on polycyclic This paper presents an in-depth investigation associated with trinomials. Our results include number facts about trinomials, properties codes, new quantum derived from We also state several conjectures pol...

In this note we determine weight distributions of minimal constacyclic codes of length p over the finite field Fl, where p is a prime which is coprime to l.

Recently, a new algorithm to test equivalence of two cyclic codes has been introduced which is efficient and produced useful results. In this work, we generalize constacyclic codes. As an application the found many with good parameters properties. particular, 22 that improve minimum distances best known linear (BKLCs).

We generalize the construction of linear codes via skew polynomial rings by using Galois rings instead of finite fields as coefficients. The resulting non commutative rings are no longer left and right Euclidean. Codes that are principal ideals in quotient rings of skew polynomial rings by a two sided ideals are studied. As an application, skew constacyclic self-dual codes over GR(4) are constr...

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...

Recently, Yaakobi et al. introduced codes for b-symbol read channels, where the read operation is performed as a consecutive sequence of b > 2 symbols. In this paper, we establish a Singleton-type bound on b-symbol codes. Codes meeting the Singleton-type bound are called maximum distance separable (MDS) codes, and they are optimal in the sense they attain the maximal minimum bdistance. Based on...

We prove that the cyclic and constacyclic codes constructed by Grassl Rötteler in International Symposium on Information Theory (ISIT), pp. 1104–1108 (2015) are generalised Reed–Solomon codes. This note can be considered as an addendum to pp (2015). It also appendix Ball Vilar IEEE Trans Inform 68:3796–3805, (2022) where Conjecture 11 of (2015), which was stated for Grassl–Rötteler codes, is pr...