A Note on Weight Distributions of Irreducible Cyclic Codes

Details A Note on Weight Distributions of Irreducible Cyclic Codes A Note on Weight Distributions of Irreducible Cyclic Codes

2012-02-16

arxiv.org/abs/1202.3514v1

Computer Science

Information Theory

Scientific paper

Usually, it is difficult to determine the weight distribution of an irreducible cyclic code. In this paper, we discuss the case when an irreducible cyclic code has the maximal number of distinct nonzero weights and give a necessary and sufficient condition. In this case, we also obtain a divisible property for the weight of a codeword. Further, we present a necessary and sufficient condition for an irreducible cyclic code with only one nonzero weight. Finally, we determine the weight distribution of an irreducible cyclic code for some cases.

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