The Weight Distribution for an Extended Family of Reducible Cyclic Codes

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• 关键词：Weight distribution ; Reducible cyclic codes ; Gaussian periods ; Cross ; correlation functions
• 刊名：Lecture Notes in Computer Science
• 出版年：2017
• 出版时间：2017
• 年：2017
• 卷：10194
• 期：1
• 页码：213-229
• 丛书名：Codes, Cryptology and Information Security
• ISBN：978-3-319-55589-8
• 卷排序：10194

文摘

The purpose of this work is to present new advances on the weight distribution of the duals of some cyclic codes with two zeros. More specifically, our contribution improves the sufficient numerical conditions that determine the weight distribution for the class of reducible cyclic codes that were studied in [19] and in [17]. Furthermore, as will be shown later, a conclusion here will be that thanks to these previous works and the present contribution, we can determine the weight distribution for an extended family of reducible cyclic codes. More specifically, we are going to determine the weight distribution for all the elements of an extended family of reducible cyclic codes that fully covers one of the open cases suggested in [20]. In addition, as will be seen further on, through our results we obtain an alternative description for one of the families of cross-correlation functions studied in [8].