Abstract :
The problem of determining Aq(n,d)Aq(n,d), the maximum cardinality of a q-ary code of length n with minimum distance at least d, is considered in some cases where corresponding MDS codes do not exist. Slight improvements of the Singleton bound are given, including Aq(q+2,q)⩽q3-3Aq(q+2,q)⩽q3-3 if q is odd, A5(7,5)⩽53-4A5(7,5)⩽53-4 and A16(18,15)⩽184-4A16(18,15)⩽184-4.
Keywords :
qq-ary code , Aq(n , d)Aq(n , d) , Singleton bound , MDS code
