Web1 de abr. de 2024 · We examine cyclic codes over a finite commutative non-chain ring ℛ = F q [ u, v] / 〈 u 2 − γ u, v 2 − ϵ v, u v − v u 〉 for γ, ϵ ∈ F q * and its relevance in the generation of optimal LCD codes and comparatively new quantum codes. It is worth noting that the ring in [21] is a specific form of our fundamental ring ℛ (for γ ... Web1 de mar. de 2024 · Let 픽q be finite field with q elements, where q be power of an odd prime p. In this paper, we determine generator polynomials of all cyclic and negacyclic codes of length 8ℓmpn over 픽q, ... On self-dual cyclic codes over finite fields, IEEE Trans. Inf. Theory 57(4) (2011) 2243–2251.
Two Dimensional $\left( \alpha,\beta \right) $-Constacyclic Codes …
Web11 de abr. de 2024 · Characterizations and constructions of such divisors are given together with their enumeration formulas. As applications, various properties of complementary dual and self-dual cyclic and negacyclic codes over finite fields are discussed in terms of SRIM and SCRIM factors of \(x^n-1\). Gervy Marie Angeles (Modelling and Applications … WebIn coding theory, self-dual codes and cyclic codes are important classes of codes which have been extensively studied. The main objects of study in this paper are self-dual … nothing changes in french
New MDS self-dual codes over finite fields SpringerLink
Web31 de ago. de 2024 · In this paper, we generalize the notion of self-orthogonal codes to σ -self-orthogonal codes over an arbitrary finite ring. Then, we study the σ -self-orthogonality of constacyclic codes of length p s over the finite commutative chain ring F p m + u F p m, where p is a prime, u 2 = 0 and σ is an arbitrary ring automorphism of F p m + u F p m. WebMaximum distance separable (MDS) self-dual codes have useful properties due to their optimality with respect to the Singleton bound and its self-duality. MDS self-dual codes … Web29 de jan. de 2012 · There is a one-to-one correspondence between -quasi-cyclic codes over a finite field and linear codes over a ring . Using this correspondence, we prove that every -quasi-cyclic self-dual code of length over a finite field can be obtained by the {\it building-up} construction, provided that char or , is a prime , and is a primitive element of . how to set up google search console