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A Class of Three-Weight Cyclic Codes
Cyclic codes are a subclass of linear codes and have applications in consumer
electronics, data storage systems, and communication systems as they have
efficient encoding and decoding algorithms. In this paper, a class of
three-weight cyclic codes over \gf(p) whose duals have two zeros is
presented, where is an odd prime. The weight distribution of this class of
cyclic codes is settled. Some of the cyclic codes are optimal. The duals of a
subclass of the cyclic codes are also studied and proved to be optimal.Comment: 11 Page
Weight distributions of cyclic codes with respect to pairwise coprime order elements
Let be an extension of a finite field with . Let
each be of order in and for .
We define a cyclic code over by
where
and . In this paper,
we present a method to compute the weights of . Further, we determine the weight distributions of the cyclic codes
and .Comment: 18 pages. arXiv admin note: substantial text overlap with
arXiv:1306.527
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