Abstract
We use techniques from linear recurring sequences, exponential sums and Gaussian sums, in order to present a set of characterizations for the one-weight irreducible cyclic codes over finite fields. Without using such techniques, a subset of these characterizations was already presented in [2]. By means of this new set of characterizations, we give an explicit expression for the number of one-weight cyclic codes, when the length and dimension are given.
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References
Lidl, R., Niederreitter, H.: Finite Fields. Cambridge Univ. Press, Cambridge (1983)
Vega, G., Wolfmann, J.: New Classes of 2-weight Cyclic Codes. Designs, Codes and Cryptography 42(3), 327–334 (2007)
Wolfmann, J.: Are 2-Weight Projective Cyclic Codes Irreducible? IEEE Trans. Inform. Theory. 51, 733–737 (2005)
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Vega, G. (2007). Determining the Number of One-Weight Cyclic Codes When Length and Dimension Are Given. In: Carlet, C., Sunar, B. (eds) Arithmetic of Finite Fields. WAIFI 2007. Lecture Notes in Computer Science, vol 4547. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73074-3_22
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DOI: https://doi.org/10.1007/978-3-540-73074-3_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73073-6
Online ISBN: 978-3-540-73074-3
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