Weight Behavior of Irreducible Cyclic BWD-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.

Two-Weight Codes Punctured from Irreducible Cyclic Codes

The weight distributions of irreducible cyclic codes of length 2m

Let m be a positive integer and q be an odd prime power. In this short communication , the weight distributions of all the irreducible cyclic codes of length 2 m over F q are determined explicitly, directly from their generating polynomials.

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...

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...