Representations by Quadratic Forms in a Finite Field of Characteristic Two

1977 ◽  
Vol 77 (1) ◽  
pp. 237-243
Author(s):  
John D. Fulton
Keyword(s):  
Finite Field ◽  
Quadratic Forms ◽  
Characteristic Two

Association schemes of quadratic forms over a finite field of characteristic two

1998 ◽  
Vol 43 (23) ◽  
pp. 1965-1968 ◽  
Author(s):  
Yangxian Wang ◽  
Chunsen Wang ◽  
Changli Ma
Keyword(s):  
Finite Field ◽  
Quadratic Forms ◽  
Association Schemes ◽  
Characteristic Two

Representations by Hermitian Forms in a Finite Field of Characteristic Two

1977 ◽  
Vol 29 (1) ◽  
pp. 169-179 ◽  
Author(s):  
John D. Fulton
Keyword(s):  
Positive Integer ◽  
Finite Field ◽  
Multiplicative Group ◽  
Group Homomorphism ◽  
Hermitian Forms ◽  
Characteristic Two ◽  
Field Automorphism

Throughout this paper, we let q = 2W,﹜ w a positive integer, and for u = 1 or 2, we let GF(qu) denote the finite field of cardinality qu. Let - denote the involutory field automorphism of GF(q2) with GF(q) as fixed subfield, where ā = aQ for all a in GF﹛q2). Moreover, let | | denote the norm (multiplicative group homomorphism) mapping of GF(q2) onto GF(q), where |a| — a • ā = aQ+1.

scholarly journals Quadratic form Approach for the Number of Zeros of Homogeneous Linear Recurring Sequences over Finite Fields

2017 ◽  
Vol 9 (3) ◽  
pp. 8
Author(s):  
Yasanthi Kottegoda
Keyword(s):  
Quadratic Form ◽  
Finite Field ◽  
Characteristic Polynomial ◽  
Finite Fields ◽  
Quadratic Forms ◽  
Linear Recurring Sequences ◽  
Exact Number ◽  
Number Of Zeros ◽  
Homogeneous Linear ◽  
Form Approach

We consider homogeneous linear recurring sequences over a finite field $\mathbb{F}_{q}$, based on an irreducible characteristic polynomial of degree $n$ and order $m$. Let $t=(q^{n}-1)/ m$. We use quadratic forms over finite fields to give the exact number of occurrences of zeros of the sequence within its least period when $t$ has q-adic weight 2. Consequently we prove that the cardinality of the set of zeros for sequences from this category is equal to two.

Milnor'ory and quadratic forms over fields of characteristic two

1992 ◽  
Vol 20 (4) ◽  
pp. 1087-1107 ◽  
Author(s):  
Roberto Aravire ◽  
Ricardo Baeza
Keyword(s):  
Quadratic Forms ◽  
Characteristic Two

K3 of truncated polynomial rings over fields of characteristic two

1987 ◽  
Vol 101 (3) ◽  
pp. 509-521 ◽  
Author(s):  
Janet Aisbett ◽  
Victor Snaith
Keyword(s):  
Finite Field ◽  
Polynomial Ring ◽  
Polynomial Rings ◽  
Witt Vectors ◽  
Characteristic Two

Write F for the finite field, , having 2m elements. Let W2(F) denote the Witt vectors of length two over F (for a definition, see [4] or [10], §10). Write F(q) for the truncated polynomial ring, F[t]/(tq).

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