A Note on Weight Distributions of Irreducible Cyclic Codes
نویسندگان
چکیده
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.
منابع مشابه
Hamming weights in irreducible cyclic codes
The objectives of this paper are to survey and extend earlier results on the weight distributions of irreducible cyclic codes, present a divisibility theorem and develop bounds on the weights in irreducible cyclic codes. © 2012 Elsevier B.V. All rights reserved.
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ورودعنوان ژورنال:
- Discrete Math., Alg. and Appl.
دوره 6 شماره
صفحات -
تاریخ انتشار 2014