Two strongly seminormal codes over Z/sub 5/ are constructed to prove a conjecture of Ostergard (see ibid., vol.37, no.3, p.660-4, 1991). It is shown that a result of Honkala (see ibid., vol.37, no.4, p.1203-6, 1991) on (k,t)-subnormal codes holds also under weaker assumptions. A lower bound and an upper bound on K/sub q/(n, R), the minimal cardinality of a q-ary code of length n with covering radius R are obtained. These give improvements in seven upper bounds and twelve lower bounds by Ostergard for K/sub q/(n, R) for q=3, 4, and 5.
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机译:构造了两个在Z / sub 5 /上的强半正规代码来证明Ostergard的猜想(参见同上,第37卷,第3期,第660-4页,1991年)。结果表明,在较弱的假设下,Honkala(见同上,第37卷,第4期,第1203-6页,1991年)关于(k,t)-次正规码的结果也成立。获得K / sub q /(n,R)的下限和上限,即长度为n的q元代码的最小基数,其覆盖半径为R。对于K / sub q /(n,R),当q = 3、4和5时,Ostergard改善了七个上限和十二个下限。
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