‎we obtain the porc formulae for the number of non-associative algebras‎ ‎of dimension 2‎, ‎3 and 4 over the finite field gf$(q)$‎. ‎we also give some‎ ‎asymptotic bounds for the number of algebras of dimension $n$ over gf$(q)$‎.

‎we obtain the porc formulae for the number of non-associative algebras‎ ‎of dimension 2‎, ‎3 and 4 over the finite field gf$(q)$‎. ‎we also give some‎ ‎asymptotic bounds for the number of algebras of dimension $n$ over gf$(q)$.

We investigate the linear complexity and the minimal polynomial over the finite fields of the characteristic sequences of cubic and biquadratic residue classes. Also we find the linear complexity and the minimal polynomial of the balanced cyclotomic sequences of order three. Keywords—linear complexity, finite field, cubic residue classes, biquadratic residue classes

Let B ∈ Z[x] be a polynomial with b = B(0). Let S be a complete residue class modulo b containing 0. We attempt to classify the polynomials B and residue classes S so that for every polynomial P ∈ Z[x] there exists a polynomial Q with coefficients in S such that P ≡ Q (mod B).

In this thesis we discuss how to find equivalent representations of polynomial functions over the ring of integers modulo a power of a prime. Specifically, we look for lower degree representations and representations with fewer variables for which important applications in electrical and computer engineering exist. We present several algorithms for finding these compact formulations. INDEX WORD...

In this article, we investigate the construction of lightweight MDS matrices over the matrix polynomial residue ring. According to distributions of the minimum polynomial, distributions of XOR count and equivalence classes of MDS matrices, we propose an algorithm, which not only can construct lightest MDS matrices, but also is evidently more efficient than previous methods. Moreover, we investi...

Abstract We compute the number of points over finite fields character stack associated to a compact surface group and reductive with connected centre. find that answer is polynomial on residue classes (PORC). The key ingredients in proof are Lusztig’s Jordan decomposition complex characters groups Deriziotis’s results their genus numbers. As consequence our main theorem, we obtain an expression...