2 research outputs found
Several families of ternary negacyclic codes and their duals
Constacyclic codes contain cyclic codes as a subclass and have nice algebraic
structures. Constacyclic codes have theoretical importance, as they are
connected to a number of areas of mathematics and outperform cyclic codes in
several aspects. Negacyclic codes are a subclass of constacyclic codes and are
distance-optimal in many cases. However, compared with the extensive study of
cyclic codes, negacyclic codes are much less studied. In this paper, several
families of ternary negacyclic codes and their duals are constructed and
analysed. These families of negacyclic codes and their duals contain
distance-optimal codes and have very good parameters in general
Recent progress on weight distributions of cyclic codes over finite fields
Cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems due to their efficient encoding and decoding algorithms. In coding theory it is often desirable to know the weight distribution of a cyclic code to estimate the error correcting capability and error probability. In this paper, we present the recent progress on the weight distributions of cyclic codes over finite fields, which had been determined by exponential sums. The cyclic codes with few weights which are very useful are discussed and their existence conditions are listed. Furthermore, we discuss the more general case of constacyclic codes and give some equivalences to characterize their weight distributions