For any non-trivial abelian group A under addition a graph $G$ is said to be $A$-textit{magic}  if there exists a labeling $f:E(G) rightarrow A-{0}$ such that, the vertex labeling $f^+$  defined as $f^+(v) = sum f(uv)$ taken over all edges $uv$ incident at $v$ is a constant. An $A$-textit{magic} graph $G$ is said to be $Z_k$-magic graph if the group $A$ is $Z_k$  the group of integers modulo $k...

In a recent paper, Calkin et al. [N. Calkin, N. Drake, K. James, S. Law, P. Lee, D. Penniston and J. Radder, ‘Divisibility properties of the 5-regular and 13-regular partition functions’, Integers 8 (2008), #A60] used the theory of modular forms to examine 5-regular partitions modulo 2 and 13-regular partitions modulo 2 and 3; they obtained and conjectured various results. In this note, we use ...

| In this paper we present classes of algebraic interleavers that permute a sequence of bits with nearly the same statistical distribution as a randomly chosen interleaver. When these interleavers are used in turbo-coding, they perform equal to or better than the average of a set of randomly chosen interleavers. They are based on a property of quadratic congruences over the ring of integers mod...

Let G be a series-parallel graph with integer edge weights. A p-coloring of G is a mapping of vertices of G into Zp (ring of integers modulo p) so that the distance between colors of adjacent vertices u and v is at least the weight of the edge uv. We describe a quadratic time p-coloring algorithm where p is either twice the maximum edge weight or the largest possible sum of three weights of edg...

A number field modulo its ring of integers is a torus, and the units act on this torus as hyperbolic toral automorphisms. We show sufficient control over the distribution of the rational orbits to give a new, non-computational proof that Q( √ 2 + √ 2) is a normEuclidean number field, and an improved upper bound for the Euclidean minima of real cyclotomic fields of power of 2 conductor.

Abstract Let R be a finite commutative ring. The set $${{\mathcal{F}}}(R)$$ F ( R ) of polynomial functions on is ring with pointwise operations. Its group units $${{\mathcal{F}}}(R)^\times $$ × j...

In this paper, we investigate self-dual codes over finite rings, specifically the ring Z2m of integers modulo 2m . Type II codes over Z2m are introduced as self-dual codes with Euclidean weights which are a multiple of 2m+1. We describe a relationship between Type II codes and even unimodular lattices. This relationship provides much information on Type II codes. Double circulant Type II codes ...

The number-theoretic code is a class of codes defined by single or multiple congruences. These are mainly used for correcting insertion and deletion errors, asymmetric errors. This paper presents formula generalization the complete weight enumerator codes. allows us to derive enumerators cardinalities As special case, this provides Hamming non-binary Tenengolts’ codes, deletion. Moreover, we sh...

Fix pairwise coprime positive integers p1, p2, . . . , ps. We propose representing integers u modulo m, where m is any positive integer up to roughly √ p1p2 · · · ps, as vectors (u mod p1, u mod p2, . . . , u mod ps). We use this representation to obtain a new result on the parallel complexity of modular exponentiation: there is an algorithm for the Common CRCW PRAM that, given positive integer...