The weight Enumerator of some irreducible cyclic codes
This work addresses a long-standing gap in coding theory by providing weight distributions for irreducible cyclic codes, which is incremental as it focuses on a specific class rather than a broad breakthrough.
The authors tackled the problem of determining weight distributions for irreducible cyclic codes, a class where such distributions were previously known only in a few cases, and they successfully determined these distributions for a specific class, finding that the number of distinct nonzero weights varies among 1, 2, 3, 6, and 8.
Irreducible cyclic codes are one of the largest known classes of block codes which have been investigated for a long time. However, their weight distributions are known only for a few cases. In this paper, a class of irreducible cyclic codes are studied and their weight distributions are determined. Moreover, all codewords of some irreducible cyclic codes are obtained through programming in order to explain their distributions. The number of distinct nonzero weights in these codes dealt with in this paper varies among 1,2,3,6,8.