Swan's theorem for binary tetranomials

Authors:
Alfred W. Hales;Donald W. Newhart
Affiliations:
IDA/CCR La Jolla, San Diego, CA 92121, USA;National Security Agency, 9800 Savage Road, Suite 6515, Ft. George Meade, MD 21075-6515, USA
Venue:
Finite Fields and Their Applications
Year:
2006

Citing 2
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Abstract

Swan's theorem [Pacific J. Math. 12 (1962) 1099-1106] determines the parity of the number of irreducible factors of a binary trinomial. This paper does the same for a binary tetranomial. When phrased in terms of the periodic portion of the factor-parity sequence, the result in several cases is comparable in simplicity to Swan's result for square-free trinomials.