Nonexistence Theorems on Perfect Lee Codes over Large Alphabets
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Perfect codes in the Lee metric are proved to be impossible for ( 3 ⩽ n ⩽ 5 ; e ⩾ n − 1 ; q ⩾ 2 e + 1 ) and ( n ⩾ 6 ; e ⩾ 1 2 n 2 − 3 4 2 − 1 2 ; q ⩾ 2 e + 1 ) . .
[1] L. A. Bassalygo. A necessary condition for the existence of perfect codes in Lie metric , 1974 .
[2] Elwyn R. Berlekamp,et al. Algebraic coding theory , 1984, McGraw-Hill series in systems science.