The construction for several few-weight linear codes and their applications
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In this paper, for any odd prime p and an integer m≥ 3, several classes of linear codes with t-weight (t=3,5,7) are obtained based on some defining sets, and then their complete weight enumerators are determined explicitly by employing Gauss sums and quadratic character sums. Especially, for m = 3, a class of MDS codes with parameters [p,3,p-2] are obtained. Furthermore, some of these codes can be suitable for applications in secret sharing schemes and s-sum sets for any odd s>1.
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