Division of Trinomials by Pentanomials over F2 and Orthogonal Arrays
نویسندگان
چکیده
Let C f n denote the set of all subintervals of a binary shift-register sequence with length n generated by a primitive polynomial f of degree m, where m< n≤ 2m, together with the zero vector of length n. Munemasa [8] showed that if the polynomial f is a trinomial, then C f n corresponds to an orthogonal array of strength 2. His result is based on a proof that very few trinomials of degree at most 2m are divisible by the given trinomial f . We consider the case in which the sequence is generated by a pentanomial f . Our main result is that no trinomial of degree at most 2m is divisible by the given pentanomial f , provided that f is not in a finite list of exceptions we give. As a consequence, we get that C f n corresponds to an orthogonal array of strength 3.
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