New classes of 2-weight cyclic codes
Designs, Codes and Cryptography
On subfield subcodes of modified Reed-Solomon codes (Corresp.)
IEEE Transactions on Information Theory
Some two-weight codes with composite parity-check polynomials (Corresp.)
IEEE Transactions on Information Theory
Are 2-weight projective cyclic codes irreducible?
IEEE Transactions on Information Theory
The Weight Enumerator of a Class of Cyclic Codes
IEEE Transactions on Information Theory
Two-weight cyclic codes constructed as the direct sum of two one-weight cyclic codes
Finite Fields and Their Applications
Weight distribution of some reducible cyclic codes
Finite Fields and Their Applications
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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.