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

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 the distance distribution of duals of BCH codes

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/