Classical and Quantum Evaluation Codesat the Trace Roots

We introduce a new class of evaluation linear codes by evaluating polynomials at the roots of a suitable trace function. We give conditions for self-orthogonality of these codes and their subfield-subcodes with respect to the Hermitian inner product. They allow us to construct stabilizer quantum codes over several finite fields which substantially improve the codes in the literature. For the binary case, we obtain records at http://codetables.de/. Moreover, we obtain several classical linear codes over the field F 4 which are records at http://codetables.de/

New Quantum Codes from Evaluation and Matrix-Product Codes

Stabilizer codes obtained via CSS code construction and Steane's enlargement of subfield-subcodes and matrix-product codes coming from generalized Reed-Muller, hyperbolic and affine variety codes are studied. Stabilizer codes with good quantum parameters are supplied, in particular, some binary codes of lengths 127 and 128 improve the parameters of the codes in http://www.codetables.de. Moreover, non-binary codes are presented either with parameters better than or equal to the quantum codes obtained from BCH codes by La Guardia or with lengths that can not be reached by them

List decoding of repeated codes

Assuming that we have a soft-decision list decoding algorithm of a linear code, a new hard-decision list decoding algorithm of its repeated code is proposed in this article. Although repeated codes are not used for encoding data, due to their parameters, we show that they have a good performance with this algorithm. We compare, by computer simulations, our algorithm for the repeated code of a Reed-Solomon code against a decoding algorithm of a Reed-Solomon code. Finally, we estimate the decoding capability of the algorithm for Reed-Solomon codes and show that performance is somewhat better than our estimates

Stabilizer quantum codes from JJ-affine variety codes and a new Steane-like enlargement

New stabilizer codes with parameters better than the ones available in the literature are provided in this work, in particular quantum codes with parameters $[[127,63, \geq 12]]_2$ and $[[63,45, \geq 6]]_4$ that are records. These codes are constructed with a new generalization of the Steane's enlargement procedure and by considering orthogonal subfield-subcodes --with respect to the Euclidean and Hermitian inner product-- of a new family of linear codes, the $J$-affine variety codes

The Dimension of Subcode-Subfields of Shortened Generalized Reed Solomon Codes

Reed-Solomon (RS) codes are among the most ubiquitous codes due to their good parameters as well as efficient encoding and decoding procedures. However, RS codes suffer from having a fixed length. In many applications where the length is static, the appropriate length can be obtained by an RS code by shortening or puncturing. Generalized Reed-Solomon (GRS) codes are a generalization of RS codes, whose subfield-subcodes are extensively studied. In this paper we show that a particular class of GRS codes produces many subfield-subcodes with large dimension. An algorithm for searching through the codes is presented as well as a list of new codes obtained from this method

Use of informal mobile telephony in low income households in Colombia

Access to mobile telephony in Colombia exhibits rather interesting features compared to other countries. Colombia witnessed the beginning of a new alternative for communication consisting in the use of informal resale of minutes on the streets and small stores during the first years of this century. In this paper we are interested in analyzing the main factors that determine the utilization of this kind of service. We use a probabilistic model to explain the characteristics of the people that use `informal resale´ on the streets and we find that people in the modality of prepayment and people from small cities has a higher probability of using this alternative. It is also found that people in the firm-leader use more often this service. These results seem indicate that price differentials among on-net and off-net and between prepaid and postpaid are the causes of the rise of this economic activity.***El acceso a la telefonía móvil en Colombia evidencia ciertas particularidades con respecto a otros países. En Colombia surgió una nueva alternativa de comunicación que consistía en la venta de minutos de celular en las calles y en pequeños negocios durante los primeros años de ésta década. En este documento se analizan las principales características de quienes usan esta modalidad de comunicación con base en una encuesta dirigida a usuarios y no usuarios de bajos ingresos. Se usa un modelo probabilístico para explicar las características de las personas que lo usan y se encuentra que las personas que están en la modalidad de contrato prepago y que viven en ciudades pequeñas tienen una mayor probabilidad de usar esta alternativa de comunicación. De otro lado se encuentra que quienes están con el operador dominante tienden a usar este servicio también de una forma más notoria. Estos resultados parecen indicar que los diferenciales de precios entre las llamadas off-net y on-net así como entre prepago y postpago son los que alimentaron el surgimiento de esta actividad.Mobile telephony, ICT, gender gap, Resale