1. The nonexistence of ternary <f>[97,6,63]</f> codes
- Author
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Hamada, Noboru and Helleseth, Tor
- Subjects
- *
LINEAR systems , *TERNARY system - Abstract
It has been shown by Gulliver (Discrete Math. 149 (1996) 83) that there exists a ternary
[98,6,63] code. But it is unknown whether or not there exists a ternary[97,6,63] code. The purpose of this paper is to prove that there is no ternary[97,6,63] code using the structure of a{267,87;5,3} -minihyper and a generator matrix of a ternary[97,6,63] code. Sincen3(6,63)=97 or98 andd3(97,6)=62 or63 , this implies thatn3(6,63)=98 andd3(97,6)=62 , wheren3(k,d) andd3(n,k) denote the smallest value ofn and the largest value ofd , respectively, for which there exists an[n,k,d] code over the Galois fieldGF(3) . [Copyright &y& Elsevier]- Published
- 2002
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