On spectra of BCH codes

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 Primitive BCH Codes with Unequal Error Protection Capabilities

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

New Bounds on the Distance Distribution of Extended Goppa Codes

AbstractWe derive new estimates for the error term in the binomial approximation to the distance distribution of extended Goppa codes. This is an improvement on the earlier bounds by Vladuts and Skorobogatov, and Levy and Litsyn

Hecke operators and the weight distributions of certain codes

We obtain the weight distributions of the Melas and Zetterberg codes and the double error correcting quadratic Goppa codes in terms of the traces of certain Hecke operators acting on spaces of cusp forms for the congruence subgroupΓ1(4) ⊂ SL2(Z). The result is obtained from a description of the weight distributions of the dual codes in terms of class numbers of binary quadratic forms and a combination of the Eichler Selberg Trace Formula with the MacWilliams identities

Weights in Codes and Genus 2 Curves

We discuss a class of binary cyclic codes and their dual codes. The minimum distance is determined using algebraic geometry, and an application of Weil's theorem. We relate the weights appearing in the dual codes to the number of rational points on a family of genus 2 curves over a finite field