an injective map f : e(g) → {±1, ±2, · · · , ±q} is said to be an edge pair sum labeling of a graph g(p, q) if the induced vertex function f*: v (g) → z − {0} defined by f*(v) = (sigma e∈ev) f (e) is one-one, where ev denotes the set of edges in g that are incident with a vetex v and f*(v (g)) is either of the form {±k1, ±k2, · · · , ±kp/2} or {±k1, ±k2, · · · , ±k(p−1)/2} u {k(p+1)/2} accordin...

For a positive integer m and a subgroup Λ of the unit group (Z/mZ)×, the corresponding generalized Kloosterman sum is the function K(a, b,m,Λ) = ∑ u∈Λ e( au+bu−1 m ). Unlike classical Kloosterman sums, which are real valued, generalized Kloosterman sums display a surprising array of visual features when their values are plotted in the complex plane. In a variety of instances, we identify the pr...

In [5] an efficient pseudo-random number generator (PRNG) with provable security is described. Its security is based on the hardness of the subset sum or knapsack problem. In this paper we refine these ideas to design a PRNG with independent seed and output generation. This independence allows for greater parallelism, design flexibility, and possibly greater security. University of New Mexico, ...

Coding for the synchronous noiseless T-user real adder channel is considered by employing cyclic codes with symbols from an arbitrary finite integer ring. The code construction is based on the factorisation of Y 1 over the unit ring of an appropriate extension of a finite integer ring. Any number of users in the system can be independently active and the maximum achievable sum rate is 1 (when a...