Related papers: Corrigendum to New Generalized Cyclotomic Binary S…
Polynomially-recursive sequences generally have a periodic behavior mod $m$. In this paper, we analyze the period mod $m$ of a second order polynomially-recursive sequence. The problem originally comes from an enumeration of avoiding…
The autocorrelation values of two classes of binary sequences are shown to be good in [6]. We study the 2-adic complexity of these sequences. Our results show that the 2-adic complexity of such sequences is large enough to resist the attack…
This paper presents some basic theorems giving the structure of cyclic codes of length n over the ring of integers modulo p^a and over the p-adic numbers, where p is a prime not dividing n. An especially interesting example is the 2-adic…
In this paper, we study some new factorizations of period-doubling sequences over a $k$-letter alphabet, where $k\geq 2$. First, we define the combinatorial and arithmetic properties of these sequences. Then, we define the kernel words of…
In this survey we summarize properties of pseudorandomness and non-randomness of some number-theoretic sequences and present results on their behaviour under the following measures of pseudorandomness: balance, linear complexity,…
Applying a method of Godsil and McKay \cite{GM} to some graphs related to the symplectic graph, a series of new infinite families of strongly regular graphs with parameters…
We investigate the interrelationships of three notions of primary units in the local cyclotomic field of $p$-th roots of~1($p$ being an odd prime number), especially with reference to global units.
Cyclic codes are an interesting subclass of linear codes and have been used in consumer electronics, data transmission technologies, broadcast systems, and computer applications due to their efficient encoding and decoding algorithms. In…
This work is meant to demonstrate new class of prime numbers -- cyclic prime numbers, that can be derived from any prime number at certain numeric systems. Cyclic prime numbers are also related to the cyclic numbers and full reptend prime…
Let b be an odd integer such that b=+/-1 (mod 8) and let q be a prime with primitive root 2 such that q does not divide b. We show that if (p(k)) is a sequence of odd primes, with 0<=k<=q-2 such that p(k)=2p(k-1)+b for all 1<=k<=q-2, then…
This article presents a validation of a recently proposed strongly polynomial-time algorithm for the general linear programming problem. The proposed algorithm is an implicit reduction procedure that combines primal and dual linear…
Complex periods are algebraic integrals over complex algebraic domains, also appearing as Feynman integrals and multiple zeta values. The Grothendieck-de Rham period isomorphisms for p-adic algebraic varieties defined via Monski-Washnitzer…
Cyclic codes, as a crucial subclass of linear codes, exhibit broad applications in communication systems, data storage systems, and consumer electronics, primarily attributed to their well-structured algebraic properties. Let $p$ denote an…
We present the results of a comprehensive theoretical investigation on the Period-Radius (PR) relation of classical Cepheids based on new sequences of full amplitude, nonlinear convective models constructed by adopting a wide range of both…
The cyclic codes with parity check polynomial the reciprocal of the characteristic polynomial of the Fibonacci recurrence over a prime finite field are shown to have either one weight or two weights. When these codes are irreducible cyclic…
A novel generalization of the Prouhet-Thue-Morse sequence to binary $\pm 1$-weight sequences is presented. Derived from Rademacher functions, these weight sequences are shown to satisfy interesting orthogonality and recurrence relations. In…
New exceptional (i.e. non-repeating) prime number multiplets are given and formulated in terms of arithmetic progressions, along with laws governing them. Accompanying repeating prime number multiplets are pointed out. Prime number…
Let $p$ be an odd prime with $2$-adic expansion $\sum_{i=0}^kp_i\cdot2^i$. For a sequence $\underline{a}=(a(t))_{t\ge 0}$ over $\mathbb{F}_{p}$, each $a(t)$ belongs to $\{0,1,\ldots, p-1\}$ and has a unique $2$-adic expansion…
In this paper, we give an explicit expression for a certain family of ternary cyclotomic polynomials: specifically $\Phi_{p_{1}p_{2}p_{3}}$, where $p_{1}<p_{2}<p_{3}$ are odd primes such that $p_{2} \equiv1 \mod p_{1}$ and $p_{3} \equiv1…
This paper shows that $p$ primary components of certain generic crossed products are not crossed products. This applies in particular to primary components of prime degree, thus producing examples of division algebras of prime degree that…