A characterization of some {3vμ + 1, 3vμ; k - 1, q}-minihypers and some [n, k, qk-1 - 3qμ; q]-codes (k ⩾ 3, q ⩾ 5, 1 ⩽ μ < k - 1) meeting the Griesmer bound

On weighted { δv μ + 1 , δv μ ; k − 1 , q } - minihypers , q square

Weighted minihypers have recently received a lot of attention. They originated as geometrical equivalents of linear codes meeting the Griesmer bound, but have also been investigated for their importance in solving geometrical problems. Storme characterized weighted {δ(q+1), δ; k−1, q}-minihypers, q square, as a sum of lines and Baer subgeometries PG(3, √ q), provided δ is sufficiently small. Th...

On the Rational Recursive Sequence X_{N+1}=ƔX_{N-K}+(AX_N+BX_{N-K})⁄(CX_N-DX_{N-K})

Characterization of $G_2(q)$, where $2 < q equiv 1(mod 3)$ by order components

In this paper we will prove that the simple group $G_2(q)$, where $2 < q equiv 1(mod3)$ is recognizable by the set of its order components, also other word we prove that if $G$ is a finite group with $OC(G)=OC(G_2(q))$, then $G$ is isomorphic to $G_2(q)$.

On the family of Diophantine triples { k − 1 , k + 1 , 16 k 3 − 4 k }

It is proven that if k ≥ 2 is an integer and d is a positive integer such that the product of any two distinct elements of the set {k − 1, k + 1, 16k − 4k, d} increased by 1 is a perfect square, then d = 4k or d = 64k−48k+8k. Together with a recent result of Fujita, this shows that all Diophantine quadruples of the form {k − 1, k + 1, c, d} are regular.

Cyclic codes of arbitrary length over F q + uF q + u 2 F q + . . . + u k − 1 F

In this paper, we study the structure of cyclic codes of an arbitrary length n over the ring Fq + uFq + uFq + . . . + uFq, where u = 0 and q is a power of prime. Also we study the rank for these codes, and we find their minimal spanning sets. This study is a generalization and extension of the works in references [9] and [12], the dual codes over the ring Fq + uFq + uFq, where u3 = 0 are studie...