Projective two-weight irreducible cyclic and constacyclic codes

Two-Weight Codes Punctured from Irreducible Cyclic Codes

Weight enumerator of some irreducible cyclic codes

In this article, we show explicitly all possible weight enumerators for every irreducible cyclic code of length n over a finite field Fq, in the case which each prime divisor of n is also a divisor of q − 1.

A class of cyclic codes constructed via semiprimitive two-weight irreducible cyclic codes∗

We present a family of reducible cyclic codes constructed as a direct sum (as vector spaces) of two different semiprimitive two-weight irreducible cyclic codes. This family generalizes the class of reducible cyclic codes that was reported in the main result of [10]. Moreover, despite of what was stated therein, we show that, at least for the codes studied here, it is still possible to compute t...

On the weight distribution of the duals of irreducible cyclic codes, cyclic codes with two zeros and hyper-Kloosterman codes

This paper considers the weight distributions of binary cyclic codes with one or two zeros and hyper-Kloosterman codes. The results on value distributions of certain monomial exponential sums and connections between exponential sums and Kloosterman sums are applied together with the Pless power moment identity in these conciderations. Explicit formulae for the number of low-weight codewords are...

A Note on Weight Distributions of Irreducible Cyclic Codes

Usually, it is difficult to determine the weight distribution of an irreducible cyclic code. In this paper, we discuss the case when an irreducible cyclic code has the maximal number of distinct nonzero weights and give a necessary and sufficient condition. In this case, we also obtain a divisible property for the weight of a codeword. Further, we present a necessary and sufficient condition fo...