Abstract
A remarkably general result which provides the evaluation of a family of exponential sums was presented by Marko J. Moisio (Acta Arithmetica, 93 (2000) 117-119). In this work, we use a particular instance of this general result in order to determine the value distribution of a particular exponential sum. Then, motivated by some new and fresh original ideas of Changli Ma, Liwei Zeng, Yang Liu, Dengguo Feng and Cunsheng Ding (IEEE Trans. Inf. Theory, 57-1 (2011) 397-402), we use this value distribution in order to obtain the weight distribution of a family of reducible cyclic codes. As we will see later, all the codes in this family are non-projective cyclic codes. Furthermore, they can be identified in a very easy way. In fact, as a by-product of this easy identification, we will be able to determine the exact number of cyclic codes in a family when length and dimension are given.
Partially supported by PAPIIT-UNAM IN105611.
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Vega, G., Vázquez, C.A. (2012). The Weight Distribution of a Family of Reducible Cyclic Codes. In: Özbudak, F., Rodríguez-Henríquez, F. (eds) Arithmetic of Finite Fields. WAIFI 2012. Lecture Notes in Computer Science, vol 7369. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31662-3_2
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DOI: https://doi.org/10.1007/978-3-642-31662-3_2
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