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...

In this work the definition of codes as modules over skew polynomial rings of automorphism type is generalized to skew polynomial rings, whose multiplication is defined using an automorphism and a derivation. This produces a more general class of codes which, in some cases, produce better distance bounds than module skew codes constructed only with an automorphism. Extending the approach of Gab...

In this work, we study a class of generalized quasi-cyclic (GQC) codes called skew GQC codes. By the factorization theory of ideals, we give the Chinese Remainder Theorem over the skew polynomial ring, which leads to a canonical decomposition of skew GQC codes. We also focus on some characteristics of skew GQC codes in details. For a 1-generator skew GQC code, we define the parity-check polynom...

Quantum error-correcting codes have gained prominence since the initial discovery of Shor and Steane. In 1998, Calderbank et al. presented systematic methods to construct binary quantum codes, called stabilizer codes or additive codes, from classical error-correcting codes. Since then the field has made rapid progress, many good binary quantum codes were constructed by using classical error-cor...

In this study, we consider linear and especially cyclic codes over the non-chain ring Zp[v]/〈v − v〉 where p is a prime. This is a generalization of the case p = 3. Further, in this work the structure of constacyclic codes are studied as well. This study takes advantage mainly from a Gray map which preserves the distance between codes over this ring and p-ary codes and moreover this map enlighte...

‎‎a natural generalization of two dimensional cyclic code ($t{tdc}$) is two dimensional skew cyclic code‎. ‎it is well-known that there is a correspondence between two dimensional skew cyclic codes and left ideals of the quotient ring $r_n:=f[x,y;rho,theta]/_l$‎. ‎in this paper we characterize the left ideals of the ring $r_n$ with two methods and find the generator matrix for two dimensional s...