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Five Families of Three-Weight Ternary Cyclic Codes and Their Duals
As a subclass of linear codes, cyclic codes have applications in consumer
electronics, data storage systems, and communication systems as they have
efficient encoding and decoding algorithms. In this paper, five families of
three-weight ternary cyclic codes whose duals have two zeros are presented. The
weight distributions of the five families of cyclic codes are settled. The
duals of two families of the cyclic codes are optimal
A Family of Five-Weight Cyclic Codes and Their Weight Enumerators
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 family of -ary
cyclic codes whose duals have three zeros are proposed. The weight distribution
of this family of cyclic codes is determined. It turns out that the proposed
cyclic codes have five nonzero weights.Comment: 14 Page
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