127 research outputs found
On the Divisibility of Trinomials by Maximum Weight Polynomials over F2
Divisibility of trinomials by given polynomials over finite fields has been
studied and used to construct orthogonal arrays in recent literature. Dewar et
al.\ (Des.\ Codes Cryptogr.\ 45:1-17, 2007) studied the division of trinomials
by a given pentanomial over \F_2 to obtain the orthogonal arrays of strength
at least 3, and finalized their paper with some open questions. One of these
questions is concerned with generalizations to the polynomials with more than
five terms. In this paper, we consider the divisibility of trinomials by a
given maximum weight polynomial over \F_2 and apply the result to the
construction of the orthogonal arrays of strength at least 3.Comment: 10 pages, 1 figur
Zero divisors of support size in group algebras and trinomials divided by irreducible polynomials over
A famous conjecture about group algebras of torsion-free groups states that
there is no zero divisor in such group algebras. A recent approach to settle
the conjecture is to show the non-existence of zero divisors with respect to
the length of possible ones, where by the length we mean the size of the
support of an element of the group algebra. The case length cannot be
happen. The first unsettled case is the existence of zero divisors of length
. Here we study possible length zero divisors in rational group algebras
and in the group algebras over the field with elements for some prime
Pseudonoise sequence generation with three-tap linear feedback shift registers
Pseudonoise sequence generation with three-tap linear feedback shift register
Testing Irreducibility of Trinomials over GF(2)
The focus of this paper is testing the irreducibility of polynomials over finite fields. In particular there is an emphasis on testing trinomials over the finite field GF(2). We also prove a the probability of a trinomial satisfying Swan\u27s theorem is asymptotically 5/8 as n goes to infinity
Periodic binary sequence generators: VLSI circuits considerations
Feedback shift registers are efficient periodic binary sequence generators. Polynomials of degree r over a Galois field characteristic 2(GF(2)) characterize the behavior of shift registers with linear logic feedback. The algorithmic determination of the trinomial of lowest degree, when it exists, that contains a given irreducible polynomial over GF(2) as a factor is presented. This corresponds to embedding the behavior of an r-stage shift register with linear logic feedback into that of an n-stage shift register with a single two-input modulo 2 summer (i.e., Exclusive-OR gate) in its feedback. This leads to Very Large Scale Integrated (VLSI) circuit architecture of maximal regularity (i.e., identical cells) with intercell communications serialized to a maximal degree
- …