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In this paper, we present linear systematic error-correcting codes $\mathcal{L}_{k}$ and $\mathcal{L}^{+}_{k}$ which are the results of our research on the sub-exceeding functions. Given an integer $ k $ such that $ k \geq 3$, these two codes are respectively $[2k,k]$ and $[3k,k]$ linear codes. The minimum distance of $\mathcal{L}_3$ is 3 and for $k\geq 4$ the minimum distance of $\mathcal{L}_k$ is 4. The code $\mathcal{L}_k ^{+}$, the minimum distances are respectively 5 and 6 for $ k = 4 $ and $ k \geq 5 $. By calculating the complexity of the algorithms, our codes have fast and efficient decoding. Then, for a short and medium distance data transmission (wifi network, bluetooth, cable, ...), we see that the codes mentioned above present many advantages.
Field : Fen Bilimleri ve Matematik
Journal Type : Uluslararası
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