Abstmct Two soft-decision algorithms f o r decoding the (6,3,4) q u a t e r n a r y code, the hezocode, are p resented. Both algorithms have the same guaranteed error cor rec t ion radius as that of maximum-likelihood decoding. In using them, bounded-distance decoding of the Golay code and the Leech lattice are performed i n at most 187 and 519 real operations respectively. We present s o m e s...

In this paper we establish several polynomials similar to Bernstein's polynomials and several refinements of  Hermite-Hadamard inequality for convex functions.

For a two-parameter family of lower triangular matrices with entries involving Jacobi polynomials an explicit inverse is given, with entries involving a sum of two Jacobi polynomials. The formula simplifies in the Gegenbauer case and then one choice of the parameter solves an open problem in a recent paper by Koelink, van Pruijssen & Román. The twoparameter family is closely related to two two-...

Lanczos-type product methods for solving large sparse non-Hermitian linear systems have as residual polynomials either the squares of the Lanczos polynomials or the products of the latter with another sequence of polynomials, which is normally chosen to enforce some local minimization of the residual norm. In either case, these methods inherit from the underlying Lanczos process the danger of b...

Definition of the strongly regular graphs on 77 and 100 vertices belonging to the simple groups M22 and HiS.

Visual recovery after perinatal stroke evidenced by functional and diffusion MRI.

Let G = SAff(n, R) be the group of all transformations in R as F (x) = gx + b such that g ∈ SL(n, R) and b ∈ R. The system of generators for the differential algebra of all G-invariant differential polynomials of a pair of curves is found for the group SAff(n, R). The conditions for G-equivalence of a pair of curves is obtained.

This paper presents some basic theorems giving the structure of cyclic codes of length n over the ring of integers modulo pa and over the p-adic numbers, where p is a prime not dividing n. An especially interesting example is the 2-adic cyclic code of length 7 with generator polynomial X 3 + ,~X 2 + (L I)X -l, where )~ satisfies ~2 _ k + 2 = 0. This is the 2-adic generalization of both the bina...