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- W2952176699 abstract "Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. Let $m=2ell+1$ for an integer $ellgeq 1$ and $pi$ be a generator of $gf(3^m)^*$. In this paper, a class of cyclic codes $C_{(u,v)}$ over $gf(3)$ with two nonzeros $pi^{u}$ and $pi^{v}$ is studied, where $u=(3^m+1)/2$, and $v=2cdot 3^{ell}+1$ is the ternary Welch-type exponent. Based on a result on the non-existence of solutions to certain equation over $gf(3^m)$, the cyclic code $C_{(u,v)}$ is shown to have minimal distance four, which is the best minimal distance for any linear code over $gf(3)$ with length $3^m-1$ and dimension $3^m-1-2m$ according to the Sphere Packing bound. The duals of this class of cyclic codes are also studied." @default.
- W2952176699 created "2019-06-27" @default.
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- W2952176699 date "2015-10-16" @default.
- W2952176699 modified "2023-10-14" @default.
- W2952176699 title "A class of optimal ternary cyclic codes and their duals" @default.
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- W2952176699 doi "https://doi.org/10.48550/arxiv.1510.05048" @default.
- W2952176699 hasPublicationYear "2015" @default.
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