Let F r be an extension of a finite field F q with r = q m . Let each g i be of order n i in F * r and gcd(n i , n j ) = 1 for 1 ≤ i = j ≤ u. We define a cyclic code over F q by C (q,m,n1,n2,...,nu)
In this letter, we use Gauss sums of index 2 to construct a class of new binary linear codes with at most three weights. In special cases, they are optimal or near optimal codes. These codes can be used in authentication codes and secret sharing schemes.
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