5 research outputs found

    On spectra of BCH codes

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    Derives an estimate for the error term in the binomial approximation of spectra of BCH codes. This estimate asymptotically improves on the bounds by Sidelnikov (1971), Kasami et al. (1985), and Sole (1990)

    On the distance distribution of duals of BCH codes

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    We derive upper bounds on the components of the distance distribution of duals of BCH codes. Roughly speaking, these bounds show that the distance distribution can be upper-bounded by the corresponding normal distribution. To derive the bounds we use the linear programming approach along with some estimates on the magnitude of Krawtchouk polynomials of fixed degree in a vicinity of q/

    On Primitive BCH Codes with Unequal Error Protection Capabilities

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    Presents a class of binary primitive BCH codes that have unequal-error-protection (UEP) capabilities. The authors use a previous result on the span of their minimum weight vectors to show that binary primitive BCH codes, containing second-order punctured Reed-Muller (RM) codes of the same minimum distance, are binary-cyclic UEP codes. The values of the error correction levels for this class of binary LUEP codes are estimated

    Weight of duals of BCH codes and exponential sums

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    AbstractWe consider a binary BCH code Cm of length 2m–1. If m is odd, we improve the bound on the distance of the dual of Cm previously given by Carlitz–Uchiyama, Serre and Moreno–Moreno

    Covering Radius 1985-1994

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    We survey important developments in the theory of covering radius during the period 1985-1994. We present lower bounds, constructions and upper bounds, the linear and nonlinear cases, density and asymptotic results, normality, specific classes of codes, covering radius and dual distance, tables, and open problems
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