| Popis: |
In this paper, we consider q -ary codes of length n and minimum Hamming distance d , which have two weights w 1 and w 2 . These codes are denoted by ( n , d , { w 1 , w 2 } ) q codes. Let A q ( n , d , { w 1 , w 2 } ) denote the largest possible number of codewords in an ( n , d , { w 1 , w 2 } ) q code and we simply write A ( n , d , { w 1 , w 2 } ) for A 2 ( n , d , { w 1 , w 2 } ) . Some upper bounds on A q ( n , d , { w 1 , w 2 } ) are given. The equivalences between binarytwo-weight codes and special combinatorial configurations with certain properties are established and then new upper bounds on A ( n , d , { w 1 , w 2 } ) are derived. For w 1 , w 2 ∈ { 2 , 3 , 4 } , optimal constructions of ( n , d , { w 1 , w 2 } ) 2 codes are presented. The exact value of A ( n , d , { 2 , 3 } ) is completely determined for all n and d . We determine the exact value of A ( n , d , { 2 , 4 } ) for any positive integer n ≡ 2 , 4 ( mod 6 ) and d ∈ { 3 , 4 } . The exact value of A ( n , d , { 3 , 4 } ) is determined for any integer n and d ∈ { 6 , 7 } , or d = 5 and n ≡ 0 , 2 , 3 , 11 ( mod 12 ) . |
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