A note on the construction of optimal linear codes |
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Authors: | Fumikazu Tamari |
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Affiliation: | Department of Mathematics, Fukuoka University of Education, Munakata, Fukuoka, Japan |
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Abstract: | Let us denote by (n,k,d)-code, a binary linear code with code length nk information symbols and the minimum distance d. It is well known that the problem of obtaining a binary linear code whose code length n is minimum among (n,k,d)-codes for given integers k and d, is equivalent to solve a linear programming whose solutions correspond to a minimum redundancy error-correcting code. In this paper it will be shown that for some given integers d, there exists no solution of the linear programming except a solution which is obtained using a flat in a finite projective geometry. |
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Keywords: | Primary 94A10 Secondary 94A15, 90C05, 05B25 Linear Code Linear Programming Finite Projective Geometry Vector Space Max Hyper Min Hyper |
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