the paper presents the results of an investigation on the acoustic performance of vertical profile parallel barriers with quadratic residue diffuser tops and faces. a 2d boundary element method (bem) was used to predict the barrier insertion loss. the results of rigid and with absorptive coverage were also calculated for comparisons. using qrd on the top surface and faces of all vertical profil...

The Hamming weight enumerator function of the formally self-dual even, binary extended quadratic residue code of prime p = 8m + 1 is given by Gleason’s theorem for singly-even code. Using this theorem, the Hamming weight distribution of the extended quadratic residue is completely determined once the number of codewords of Hamming weight j Aj , for 0 ≤ j ≤ 2m, are known. The smallest prime for ...

A simplified algorithm for decoding binary quadratic residue (QR) codes is developed in this paper. The key idea is to use the efficient Euclidean algorithm to determine the greatest common divisor of two specific polynomials which can be shown to be the error-locator polynomial. This proposed technique differs from the previous schemes developed for QR codes. It is especially simple due to the...

A prime number p is called b-elite if only finitely many generalized Fermat numbers Fb,n = b 2 + 1 are quadratic residues to p. So far, only the case b = 2 was subjected to theoretical and experimental researches by several authors. Most of the results obtained for this special case can be generalized for all bases b > 2. Moreover, the generalization allows an insight to more general structures...

By a careful analysis of the proofs of Kopparty in fields of characteristic 2, we show that the problem of powering in Fpn requires ACC(p) circuits of exponential size (in n), for any fixed prime p > 2. Similar bounds hold for quadratic residuosity. As a corollary, we obtain non-trivial bounds for exponential sums that express the correlation between the quadratic character of Fpn and n-variate...

We determine the product of the invertible quadratic residues in Zn. This is a variation on Gauss’ generalization of Wilson’s Theorem. From this we deduce that for twin primes p, p + 2, the product of the invertible quadratic residues in Zp(p+2) is ±(p+1), where the sign depends on the residue class of p modulo 4. We examine necessary and sufficient conditions for consecutive odd natural number...

We present some observations on a restricted variant of unitary Cayley graphs modulo n, and implications for a decomposition of elements of symplectic operators over the integers modulo n. We define quadratic unitary Cayley graphs Gn, whose vertex set is the ring Zn, and where residues a, b modulo n are adjacent if and only if their difference is a quadratic residue. By bounding the diameter of...

After a brief introduction to hash-coding (scatter storage) and discussion of methods described in the literature, it is shown that for hash tables of length p >2, prime, the primitive roots r of the cyclic group Z/p of prime residues mod p can be used for a simple collision strategy q(p,i) = r mod p for fi(k) = f0(k) +q(p,i) mod p. It is similar to the strategy which uses quadratic residues q(...

A non-empty family S of subsets of a finite set A has the odd (respectively, even) intersection property if there exists non-empty B ⊆ A with |B∩S| odd (respectively, even) for each S ∈ S. In characterizing sets of integers that are quadratic nonresidues modulo infinitely many primes, Wright asked for the number of such S, as a function of |A|. We give explicit formulae.

A substructure isomorphism matrix n x p contains binary elements describing which of the given p query structures (substructures) are part of the given n target structures (molecular structures). Such a matrix can be used to investigate the diversity of the target structures and allows the characterization and comparison of structural libraries. A quadratic substructure isomorphism matrix n x n...