J. Carmelo Interlando

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Let A = (aij)k×n be a matrix with entries in the Galois field GF (2), and let x = (x1, x2, . . . , xn) be a vector of variables assuming values in GF (2). The gate complexity of A, denoted by C(A), is the minimum number of XOR gates necessary to compute the matrix-vector product Ax. In this paper it is shown that C(Hk) = 2k+1 − 2k − 2, where Hk is the(More)
An algebraic decoding algorithm for the expurgated quadratic residue code of length 41 is presented. The algorithm is guaranteed to produce the correct error-location polynomial whenever an error pattern of weight up to four occurs. An error pattern of weight five is not correctable if it is equidistant from the all-zero codeword and a codeword of weight(More)
A construction technique of nite point constellations in n-dimensional spaces from ideals in rings of algebraic integers is described. An algorithm is presented to nd constellations with minimum average energy from a given lattice. For comparison, a numerical table of lattice constellations and group codes is computed for spaces of dimension two, three, and(More)
In this work we describe a procedure to construct finite signal constellations from lattices associated to rings of algebraic integers and their ideals. The procedure provides a natural way to label the constellation points by elements of a finite field. The labeling is proven to be linear which allows, at the receiver, a fast way to map a constellation(More)