A Characterization of Some Minihypers and its Application to Linear Codes |
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Authors: | Tatsuya Maruta |
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Affiliation: | (1) Department of Information Systems, Aichi Prefectural University, Nagakute, Aichi, 480-1198, Japan |
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Abstract: | Any {f,r- 2+s; r,q}-minihyper includes a hyperplane in PG(r, q) if fr-1 + s 1 + q – 1 for 1 s q – 1, q 3, r 4, where i = (qi + 1 – 1)/ (q – 1 ). A lower bound on f for which an {f, r – 2 + 1; r, q}-minihyper with q 3, r 4 exists is also given. As an application to coding theory, we show the nonexistence of [ n, k, n + 1 – qk – 2 ]q codes for k 5, q 3 for qk – 1 – 2q – 1 < n qk – 1 – q – 1 when k > q – and for when , which is a generalization of [18, Them. 2.4]. |
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Keywords: | finite projective spaces minihypers linear codes. |
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