Abstract
From the geometrical point of view, we prove that [g 3(6, d) + 1, 6, d]3 codes exist for d = 118–123, 283–297 and that [g 3(6, d), 6, d]3 codes for d = 100, 341, 342 and [g 3(6, d) + 1, 6, d]3 codes for d = 130, 131, 132 do not exist, where \({g_3(k,\,d)=\sum_{i=0}^{k-1}\left\lceil d/3^i \right\rceil}\). These determine the exact value of n 3(6, d) for d = 100, 118–123, 130, 131, 132, 283–297, 341, 342, where n q (k, d) is the minimum length n for which an [n, k, d] q code exists.
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This is one of several papers published in Designs, Codes and Cryptography comprising the “Special Issue on Finite Geometries”.
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Maruta, T., Oya, Y. On the minimum length of ternary linear codes. Des. Codes Cryptogr. 68, 407–425 (2013). https://doi.org/10.1007/s10623-011-9593-y
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DOI: https://doi.org/10.1007/s10623-011-9593-y