A Double Circulaut Presentation for Quadratic Residue Codes
نویسنده
چکیده
Three bii linear codes of length 27 and 28 are described.They cuntaiu more vectors than any previously known codes with the samelength and miuimIm3 distance. Let gi(x) and g2(x) be the following polynomials over GF(2):
منابع مشابه
Computational Results of Duadic Double Circulant Codes
Quadratic residue codes have been one of the most important classes of algebraic codes. They have been generalized into duadic codes and quadratic double circulant codes. In this paper we introduce a new subclass of double circulant codes, called duadic double circulant codes, which is a generalization of quadratic double circulant codes for prime lengths. This class generates optimal self-dual...
متن کاملMinimal Distances in Generalized Residue Codes
A general type of linear cyclic codes is introduced as a straightforward generalization of quadratic residue codes, e-residue codes, generalized quadratic residue codes and polyadic codes. A generalized version of the well-known squareroot bound for odd-weight words is derived.
متن کاملNew extremal binary self-dual codes of length 68 from quadratic residue codes over 𝔽2 + u𝔽2 + u2𝔽2
In this correspondence, we consider quadratic double and bordered double circulant construction methods over the ring R := F2 + uF2 + uF2, where u = 1. Among other examples, extremal binary self-dual codes of length 66 are obtained by these constructions. These are extended by using extension theorems for self-dual codes and as a result 8 new extremal binary self-dual codes of length 68 are obt...
متن کاملQuadratic Residue Codes over F_p+vF_p and their Gray Images
In this paper quadratic residue codes over the ring Fp + vFp are introduced in terms of their idempotent generators. The structure of these codes is studied and it is observed that these codes share similar properties with quadratic residue codes over finite fields. For the case p = 2, Euclidean and Hermitian self-dual families of codes as extended quadratic residue codes are considered and two...
متن کاملQuadratic residue codes over a non - chain ring extension of F 2
The focus in this work is on quadratic residue codes over the ring F2+vF2. We define these codes in terms of their idempotent generators and show that these codes share the properties analogous to that of quadratic residue codes over finite fields. We study Euclidean and Hermitian self-dual families of codes as extended quadratic residue codes over F2 + vF2. Further, we obtain two optimal self-...
متن کامل