The theory of algebraic-geometric codes has been developed in the beginning of the 80's after a paper of V.D. Goppa. Given a smooth projective algebraic curve X over a finite field, there are two different constructions of error-correcting codes. The first one, called"functional", uses some rational functions on X and the second one, called"differential", involves some rational 1-forms on this ...

Juan Pablo Paz, 2 Augusto José Roncaglia, 2 and Marcos Saraceno 4 Departamento de F́ısica, FCEyN, UBA, Pabellón 1, Ciudad Universitaria, 1428 Buenos Aires, Argentina Theoretical Division, LANL, MSB213, Los Alamos, NM 87545, USA Unidad de Actividad F́ısica, Tandar, CNEA, Buenos Aires, Argentina Escuela de Ciencia y Tecnoloǵıa, Univ. Nac. Gral. San Martin, Buenos Aires, Argentina (Dated: October 15...

A double serially concatenated code with two interleaves consists of the cascade of an outer encoder, an interleaver permuting the outer codeword bits, a middle encoder, another interleaver permuting the middle codeword bits and an inner encoder whose input words are the permuted middle codewords. The construction can be generalized to h cascaded encoders separated by h – 1 interleavers, where ...

The transient flow analyzing by the frequency domain method (FDM) is computationally much faster than the method of characteristic (MOC) in the time domain. FDM needs no discretization in time and space, but requires the linearization of governing equations and boundary conditions. Hence, the FDM is only valid for small perturbations in which the system’s hydraulics is almost linear. In this st...

We analyze the operation of a four-qubit Bacon-Shor code with simultaneous continuous measurement of noncommuting gauge operators. The error syndrome in this case is monitored via time-averaged cross-correlators of the output signals. We find the logical error rate for several models of decoherence, and also find the termination rate for this quantum error detecting code. The code operation is ...

We examine the performance of quantum error correcting codes subjected to random Haar distribution transformations of weight t. Rather than requiring correction of all errors, we require some high probability that a random error is corrected. We find that, for any integer i and arbitrarily high probability p < 1, there are codes which perfectly correct errors up to weight t and can correct erro...

purpose: to report a case who had undergone lasik in his right eye and prk in the fellow eye for correction of equivalent myopia but developed progressive post-operative keratectasia only in the right eye. patient and findings: a 30-year-old man had undergone lasik in right eye 3 years ago for correction of refractive error of -1.75  -1.50@48° and prk in left eye 2 years ago for correction of r...