Commutative group codes inR4,R6,R

A note on sub-orthogonal lattices

“…Being cyclical and optimal is unlikely. In addition, the results presented here complement results obtained in [13] (not considering the initial vector problem) and extend and simplify the results obtained in [1].…”

“…Furthermore, there is a degree of freedom (n(n − 1)/2) for quadratic convergence, this freedom induces quotient group with different number of generators and can make convergency more fast in certain applications, for example in the case of spherical codes are reticulated target has some multiple minimum vectors of some canonical vector, we find a non-null pertubation as it will be more efficient. We present here a method for finding lattices with suborthogonal, our method is simpler, more general and more efficient than the one presented in [1].…”

“…A large class of the problems in the coding theory are related to the properties of the lattices, in special, with sublattices generated by orthogonal basis (suborthogonal lattices). Several authors investigated the relationship of the suborthogonal with a spherical codes, and with a q-ary codes, see [1,8,13,16,17,18]), but, of course, that does not restrict to these problems ( [2,4,5,12].…”

Constructive spherical codes in 2k dimensions

“…In higher dimensions, we compare with two TLSC implementations by Naves [33] that differ in the choice of the subcode: either with k elements or on polygon layers (Table II). In these dimensions, we have also considered EQPA codes [10] (Table III), concatenated MPSK [34, p. 36], commutative group codes (CGC) [12], [13] (Tables IV and V) and some codes from [3]. The SCHF considered in these tables We see that the performance of SCHF in R 4 is, as expected, similar to TLSC and not far from some of the best known spherical codes.…”

On Cube Tilings of Tori and Classification of Perfect Codes in the Maximum Metric

“…We say that G is an (n, e, q)-admissible structure if there exist C ∈ LP L ∞ (n, e, q) such that C G as abelian groups. 1). Since this matrix have 2e + 1 in the main diagonal, we can obtain a reduced matrix from this, by applying some elementary operations on rows, thus the result holds for n. Proof.…”