Hamming Weights in Irreducible Cyclic Codes

TL;DR

This paper surveys and extends existing results on the weight distributions of irreducible cyclic codes, introduces a divisibility theorem, and develops bounds on code weights, with applications in space communications.

Contribution

It provides new theoretical insights and bounds on the weights of irreducible cyclic codes, expanding prior research in this area.

Findings

Presented a divisibility theorem for irreducible cyclic codes

Extended previous results on weight distributions

Developed new bounds on code weights

Abstract

Irreducible cyclic codes are an interesting type of codes and have applications in space communications. They have been studied for decades and a lot of progress has been made. The objectives of this paper are to survey and extend earlier results on the weight distributions of irreducible cyclic codes, present a divisibility theorem and develop bounds on the weights in irreducible cyclic codes.