A certain system of algebraic equations over finite fields is solved.
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A connection between the “type” and rank of the quadratic forms in certain case is applied.
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The weight distribution of a class of binary cyclic codes is determined by using the connection.
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We determine another class of binary cyclic codes by using the Pless power moment identities
Abstract
For two positive integers m and k, let be a class of cyclic code of length over with three nonzeros , and for or 3, where γ is a primitive element of . When is odd, Kasami in 1971 determined the weight distributions of cyclic codes and , which is the same as that of the dual of the triple error-correcting BCH code. This paper obtains the weight distributions of and for the case of being even.