We construct a class of codes of length such that the minimum distance outside of a certain subcode is, up to a constant factor, bounded below by the square root of , a well-known property of quadratic residue codes. The construction, using the group algebra of an Abelian group and a special partition or splitting of the group, yields quadratic residue codes, duadic codes, and their generalizat...

despite of beneficial effects of antibiotics in treatments of infectious diseases, antibiotic residues in meat, milk, eggs and another products can cause serious side effects for human health. it is clear that, antibiotic residues in food stuff, cause bacterial resistance, allergic reactions, toxicity, carcinogenic effects and change of natural micro flora of intestine in consumers. so, the aim...

In this paper a new algebraic decoding approach for (17,9,5) Quadratic Residue Code is proposed by using the Inverse Free Berlekamp-MasseyAlgorithm i.e. IFBM algorithm. By using an efficient algorithm an unknown syndrome are also developed in this paper. With the help of unknown syndromes, we achieve the alternative consecutive syndromes which are needed for the application of the Berlekamp-Mas...

Let C be a binary extremal self-dual doubly-even code of length n ≥ 48. If such a code has an automorphism σ of prime order p ≥ 5 then the number of fixed points in the permutation action on the coordinates is bounded by the number of p-cycles. It turns out that large primes p, i.e. n − p small, occur extremely rarely in Aut(C). Examples are the extended quadratic residue codes. We prove that d...

The aim of this work is to compare in terms of performance, area and power dissipation, the implementations of complex FIR filters based on the following number representations: traditional two’s complement (TCS), Quadratic Residue Number System (QRNS) and radix-2j Redundant Complex Number Systems (RCNS)). The resulting implementations, designed to work at the same clock rate, show that filters...

Residue Number Systems require the selection of ring moduli whose product is greater than the predicted dynamic range of the computation being performed. The restriction that the moduli be relatively prime usually limits the set of available moduli and hence the maximum dynamic range. This is particularly the case when small moduli are to be considered for efficient hardware implementation. Sev...

This paper studies explicit and theoretical bounds for several interesting quantities in number theory, conditionally on the Generalized Riemann Hypothesis. Specifically, we improve the existing explicit bounds for the least quadratic non-residue and the least prime in an arithmetic progression. We also refine the classical conditional bounds of Littlewood for L-functions at s = 1. In particula...

1 Quadratic Congruences to Prime Moduli . . . . . . . . . . . . . . . . . . . . . . . . 1 2 Quadratic Congruences to Composite Moduli . . . . . . . . . . . . . . . . . . . . . 5 3 Some Sums of Legendre’s symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 4 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 5 Solutions . . . . . . . . . . . . ...

The pure spinor formalism for the superstring has recently been used to compute massless four-point two-loop amplitudes in a manifestly super-Poincaré covariant manner. In this paper, we show that when all four external states are Neveu-Schwarz, the two-loop amplitude coincides with the RNS result.