A generalization of Swan's theorem
Mathematics of Computation
On the Number of Trace-One Elements in Polynomial Bases for $$\mathbb{F}_{2^n}$$
Designs, Codes and Cryptography
On the Number of Trace-One Elements in Polynomial Bases for $$\mathbb{F}_{2^n}$$
Designs, Codes and Cryptography
Reducible Polynomial over $\mathbb{F}_{2}$ Constructed by Trinomial σ-LFSR
Information Security and Cryptology
Another look at square roots (and other less common operations) in fields of even characteristic
SAC'07 Proceedings of the 14th international conference on Selected areas in cryptography
A note on the reducibility of binary affine polynomials
Designs, Codes and Cryptography
Swan-like results for binomials and trinomials over finite fields of odd characteristic
Designs, Codes and Cryptography
Parity of the number of irreducible factors for composite polynomials
Finite Fields and Their Applications
On the parity of the number of irreducible factors of self-reciprocal polynomials over finite fields
Finite Fields and Their Applications
The parity of the number of irreducible factors for some pentanomials
Finite Fields and Their Applications
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Richard G. Swan proved in 1962 that trinomials x^8^k+x^m+1@?F"2[x] with 8km have an even number of irreducible factors, and so cannot be irreducible. In fact, he found the parity of the number of irreducible factors for any square-free trinomial in F"2[x]. We prove a result that is similar in spirit. Namely, suppose n is odd and f(x)=x^n+@?"i"@?"Sx^i+1@?F"2[x], where S@?{i:iodd,0