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—Let p = ef +1 be an odd prime for some e and f , and let F p be the finite field with p elements. In this paper, we explicitly describe the trace representations of the binary characteristic sequences (of period p) of all the cyclic difference sets D which are some union of cosets of eth powers H e in F 3 p (F p nf0g) for e 12. For this, we define eth… (More)