AN ALGORITHMIC APPROACH TO ACHIEVE MINIMUM $\\rho$-DISTANCE AT LEAST d IN LINEAR ARRAY CODES

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An array code/linear array code is a subset/subspace, respectively, of the linear space Matm×s(Fq), the space of all m × s matrices with entries froma finite field Fq endowed 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 numberBq(m × s, d) where Bq(m × s, d) is the largest number of code matrices possiblein a linear array code V ⊆ Mat m × s (Fq) having minimum $\\rho$-distance at least d.

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  • 九州数学雑誌

    九州数学雑誌 62 (1), 189-200, 2008

    九州大学大学院数理学研究院

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