On weights in duadic codes

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...

Cyclotomy and Duadic Codes of Prime Lengths

In this paper we present a cyclotomic approach to the construction of all binary duadic codes of prime lengths. We calculate the number of all binary duadic codes for a given prime length and that of all duadic codes that are not quadratic residue codes. We give necessary and sufficient conditions for p such that all binary duadic codes of length p are quadratic residue (Q.R.) codes. We also sh...

Iso-orthogonality and Type-II duadic constacyclic codes

Generalizing even-like duadic cyclic codes and Type-II duadic negacyclic codes, we introduce even-like (i.e.,Type-II) and odd-like duadic constacyclic codes, and study their properties and existence. We show that even-like duadic constacyclic codes are isometrically orthogonal, and the duals of even-like duadic constacyclic codes are odd-like duadic constacyclic codes. We exhibit necessary and ...

On generalized weights for codes over ℤk

On The Weights of Irreducible Cyclic Codes

The paper is devoted to the study of the weight distribution of irreducible cyclic codes. We start from the interpretation due to McEliece of these weights by means of Gauss sums. Firstly, a p-adic analysis using Stickelberger congruences and Gross-Koblitz formula enable us to improve the divisibility theorem of McEliece by giving results on the multiplicity of the weights. Secondly, in connect...