Permutation Trinomials Over Finite Fields with Even Characteristic
نویسندگان
چکیده
منابع مشابه
New Permutation Trinomials From Niho Exponents over Finite Fields with Even Characteristic
In this paper, a class of permutation trinomials of Niho type over finite fields with even characteristic is further investigated. New permutation trinomials from Niho exponents are obtained from linear fractional polynomials over finite fields, and it is shown that the presented results are the generalizations of some earlier works.
متن کاملNew classes of permutation binomials and permutation trinomials over finite fields
Permutation polynomials over finite fields play important roles in finite fields theory. They also have wide applications in many areas of science and engineering such as coding theory, cryptography, combinational design, communication theory and so on. Permutation binomials and trinomials attract people’s interest due to their simple algebraic form and additional extraordinary properties. In t...
متن کاملSymmetric bilinear forms over finite fields of even characteristic
Let Sm be the set of symmetric bilinear forms on an m-dimensional vector space over GF(q), where q is a power of two. A subset Y of Sm is called an (m, d)-set if the difference of every two distinct elements in Y has rank at least d. Such objects are closely related to certain families of codes over Galois rings of characteristic four. An upper bound on the size of (m, d)-sets is derived, and i...
متن کاملExtremal Trinomials over Quadratic Finite Fields
In the process of pursuing a finite field analogue of Descartes’ Rule, Bi, Cheng, and Rojas (2014) proved an upper bound of 2 √ q − 1 on the number of roots of a trinomial c1 + c2x a2 + c3x a3 ∈ Fq [x], conditional on the exponents satisfying δ = gcd(a2, a3, q − 1) = 1, and Cheng, Gao, Rojas, and Wan (2015) showed that this bound is near-optimal for many cases. Our project set out to refine the...
متن کاملPermutation Binomials over Finite Fields
We prove that if xm + axn permutes the prime field Fp, where m > n > 0 and a ∈ Fp, then gcd(m − n, p − 1) > √ p − 1. Conversely, we prove that if q ≥ 4 and m > n > 0 are fixed and satisfy gcd(m − n, q − 1) > 2q(log log q)/ log q, then there exist permutation binomials over Fq of the form xm + axn if and only if gcd(m,n, q − 1) = 1.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2015
ISSN: 0895-4801,1095-7146
DOI: 10.1137/140960153