1,291 research outputs found
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 accuracy of the binomial approximation to the distance distribution of codes
The binomial distribution is a well-known approximation to the distance spectra of many classes of codes. We derive a lower estimate for the deviation from the binomial approximatio
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 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/
On Pseudocodewords and Improved Union Bound of Linear Programming Decoding of HDPC Codes
In this paper, we present an improved union bound on the Linear Programming
(LP) decoding performance of the binary linear codes transmitted over an
additive white Gaussian noise channels. The bounding technique is based on the
second-order of Bonferroni-type inequality in probability theory, and it is
minimized by Prim's minimum spanning tree algorithm. The bound calculation
needs the fundamental cone generators of a given parity-check matrix rather
than only their weight spectrum, but involves relatively low computational
complexity. It is targeted to high-density parity-check codes, where the number
of their generators is extremely large and these generators are spread densely
in the Euclidean space. We explore the generator density and make a comparison
between different parity-check matrix representations. That density effects on
the improvement of the proposed bound over the conventional LP union bound. The
paper also presents a complete pseudo-weight distribution of the fundamental
cone generators for the BCH[31,21,5] code
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