263 resultados para extremal polynomials


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In this paper, we present a new construction and decoding of BCH codes over certain rings. Thus, for a nonnegative integer t, let A0 ⊂ A1 ⊂···⊂ At−1 ⊂ At be a chain of unitary commutative rings, where each Ai is constructed by the direct product of appropriate Galois rings, and its projection to the fields is K0 ⊂ K1 ⊂···⊂ Kt−1 ⊂ Kt (another chain of unitary commutative rings), where each Ki is made by the direct product of corresponding residue fields of given Galois rings. Also, A∗ i and K∗ i are the groups of units of Ai and Ki, respectively. This correspondence presents a construction technique of generator polynomials of the sequence of Bose, Chaudhuri, and Hocquenghem (BCH) codes possessing entries from A∗ i and K∗ i for each i, where 0 ≤ i ≤ t. By the construction of BCH codes, we are confined to get the best code rate and error correction capability; however, the proposed contribution offers a choice to opt a worthy BCH code concerning code rate and error correction capability. In the second phase, we extend the modified Berlekamp-Massey algorithm for the above chains of unitary commutative local rings in such a way that the error will be corrected of the sequences of codewords from the sequences of BCH codes at once. This process is not much different than the original one, but it deals a sequence of codewords from the sequence of codes over the chain of Galois rings.

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A Goppa code is described in terms of a polynomial, known as Goppa polynomial, and in contrast to cyclic codes, where it is difficult to estimate the minimum Hamming distance d from the generator polynomial. Furthermore, a Goppa code has the property that d ≥ deg(h(X))+1, where h(X) is a Goppa polynomial. In this paper, we present a decoding principle for Goppa codes constructed by generalized polynomials, which is based on modified Berlekamp-Massey algorithm.

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Pós-graduação em Engenharia Mecânica - FEIS

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Employing the method of least squares and quadratic B-spline polynomials, different statistical models were tested to identify the most appropriate to model the mean trajectories of live weight and carcass yield of Nile tilapia (Oreochromis niloticus). Data of live weight (8,758) and carcass yield (2,042) of tilapias with ages between 106 and 245 days were obtained from 72 families derived from 36 males and 72 females. The sex and tank variables were considered as classificatory and the coefficients of quadratic polynomials B-spline of two to five intervals of the same size were used as covariables. According to most fit criteria used, the models with quadratic B-spline polynomial with five intervals of the same size presented the best adjustments. The increase in number of intervals of B-spline polynomial improved the fit of the polynomials to the data. The inclusion of classificatory effects from sex, tank, the interaction of these effects and the quadratic polynomial B-spline nested in this interaction indicated that, over time, each sex, grown in different tank, presented different mean trajectory, necessitating the inclusion of nesting time in the interaction sex x tank in order to avoid the under or overestimation of breeding values of the selection candidates in breeding programs of this species.

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