Paper Info
Title
Determining the full weight distribution of any irreducible cyclic code over any finite field of dimension two.
Abstract
In coding theory, a very interesting problem (but at the same time, a very difficult one) is to determine the weight distribution of a given code. This problem is even more interesting for cyclic codes, and this is so, mainly because they possess a rich algebraic structure, which can be utilized in a variety of ways. For example, in Engineering Telecommunications, this structure is commonly employed to design very efficient coding and decoding algorithms. In this note, we are going to use a characterization of all semiprimitive two-weight irreducible cyclic codes over any finite field, recently presented in [8], in order to determine the full weight distribution of any irreducible cyclic code over any finite field of dimension two. In fact, the relevance of our results is that by means of them we can actually directly determine the full weight distribution of any irreducible cyclic code, of dimension one or two, just by knowing its length.
Year
Venue
Field
2016
arXiv: Information Theory
Discrete mathematics,Finite field,Algebra,Algebraic structure,Cyclic code,Coding (social sciences),Coding theory,Weight distribution,Decoding methods,Mathematics
DocType
Volume
Citations 
Journal
abs/1606.08510
0
PageRank 
References 
Authors
0.34
4
1
Name
Order
Citations
PageRank
Gerardo Vega111.06