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An array code/linear array code is a subset/subspace, respectively, of the linear space $ mathrm{Mat}_{m chi s} (F_q) $, the space of all $ m chi s $ matrices with entries froma finite field $ F_q $ e...ndowed with a non-Hamming metric known as the RT-metric or $\rho$-metric or $ m $-metric. In this paper, we obtain a sufficient lower bound on the number of parity check digits required to achieve minimum $\rho$-distance at least $ d $ in linear array codes using an algorithmic approach. The bound has been justified by an example. Using this bound, we also obtain a lower bound on the number$ B_q (m chi s, d) $ where $ B_q(m chi s, d) $ is the largest number of code matrices possiblein a linear array code $ V subseteq mathrm{Mat}_{m chi s} (Fq) $ having minimum $\rho$-distance at least $ d $.続きを見る
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Mendeley出力
