Geometrically uniform hyperbolic codes

In this paper we generalize the concept of geometrically uniform codes, formerly employed in Euclidean spaces, to hyperbolic spaces. We also show a characterization of generalized coset codes through the concept of G-linear codes.17319

Algebraic and Geometric Characterizations Related to the Quantization Problem of the C2,8C_{2,8} Channel

In this paper, we consider the steps to be followed in the analysis and interpretation of the quantization problem related to the $C_{2,8}$ channel, where the Fuchsian differential equations, the generators of the Fuchsian groups, and the tessellations associated with the cases $g=2$ and $g=3$, related to the hyperbolic case, are determined. In order to obtain these results, it is necessary to determine the genus $g$ of each surface on which this channel may be embedded. After that, the procedure is to determine the algebraic structure (Fuchsian group generators) associated with the fundamental region of each surface. To achieve this goal, an associated linear second-order Fuchsian differential equation whose linearly independent solutions provide the generators of this Fuchsian group is devised. In addition, the tessellations associated with each analyzed case are identified. These structures are identified in four situations, divided into two cases $(g=2$ and $g=3)$, obtaining, therefore, both algebraic and geometric characterizations associated with quantizing the $C_{2,8}$ channel.Comment: 31 pages, 9 figure

Time-varying Convolutional Encoder Better Than The Best Time-invariant Encoder

A periodically-time-varying binary (3, 2) convolutional code with period T = 2 and memory M = 1 having larger free distance than the best time-invariant (3, 2) convolutional code with M = 1 is exhibited.3931109111

Geometrically uniform hyperbolic codes

In this paper we generalize the concept of geometrically uniform codes, formerly employed in Euclidean spaces, to hyperbolic spaces. We also show a characterization of generalized coset codes through the concept of G-linear codes

On The Algebraic Fundamentals Of Convolutional Encoders Over Groups

Algebraic fundamentals of convolutional encoders are given by using the Schreier product and the Theory of Machines.30

Goppa and Srivastava codes over finite rings

Goppa and Srivastava codes over arbitrary local finite commutative rings with identity are constructed in terms of parity-cleck matrices. An efficient decoding procedure, based on the modified Berlekamp-Massey algorithm, is proposed for Goppa codes.231244Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP

Goppa and Srivastava codes over finite rings

Goppa and Srivastava codes over arbitrary local finite commutative rings with identity are constructed in terms of parity-cleck matrices. An efficient decoding procedure, based on the modified Berlekamp-Massey algorithm, is proposed for Goppa codes.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP