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Estimates of the distance distribution of codes and designs
- IEEE Trans. Inform. Theory
"... Abstract—We consider the problem of bounding the distance distribution for unrestricted block codes with known distance and/or dual distance. Applying the polynomial method, we provide a general framework for previously known results. We derive several upper and lower bounds both for finite length a ..."
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Cited by 19 (7 self)
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Abstract—We consider the problem of bounding the distance distribution for unrestricted block codes with known distance and/or dual distance. Applying the polynomial method, we provide a general framework for previously known results. We derive several upper and lower bounds both for finite length and for sequences of codes of growing length. Asymptotic results in the paper improve previously known estimates. In particular, we prove the best known bounds on the binomiality range of the distance spectrum of codes with a known dual distance. Index Terms—Binomial spectrum, constant weight codes, distance distribution, Krawtchouk polynomials, polynomial method. I.
A Lower Bound on the Distance of Cyclic Codes
, 2003
"... We present an algorithm to obtain a lower bound on the distance of cyclic codes, improving Schaub algorithm. In particular, we can provide new better bounds for the duals of binary primitive narrow-sense BCH codes of length 255. ..."
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Cited by 2 (2 self)
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We present an algorithm to obtain a lower bound on the distance of cyclic codes, improving Schaub algorithm. In particular, we can provide new better bounds for the duals of binary primitive narrow-sense BCH codes of length 255.
A Groebner Bases Technique To Compute Distance And Weight Distribution Of Cyclic Codes And Their Shortened Codes
, 2003
"... Using Grobner basis techniques, we can exhibit a method to get distance and weight distribution of both cyclic codes and shortened cyclic codes, extending and improving previous work on the distance of cyclic codes. Keywords: Grobner bases, cyclic codes, distance, weight distribution. ..."
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Cited by 1 (0 self)
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Using Grobner basis techniques, we can exhibit a method to get distance and weight distribution of both cyclic codes and shortened cyclic codes, extending and improving previous work on the distance of cyclic codes. Keywords: Grobner bases, cyclic codes, distance, weight distribution.
Estimates of the distance distribution of nonbinary codes, with applications
- in Codes and Association Schemes
, 2001
"... applications ..."
A theoretical framework for the peak-to-average power control problem in OFDM transmission
, 2004
"... ..."
Bounds for weight distribution of weakly self-dual codes
, 2008
"... Upper bounds are given for the weight distribution of binary weakly self–dual codes. To get these new bounds, we introduce a novel method of utilizing unitary operations on Hilbert spaces. This method is motivated by recent progress on quantum computing. This new approach leads to much simpler proof ..."
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Upper bounds are given for the weight distribution of binary weakly self–dual codes. To get these new bounds, we introduce a novel method of utilizing unitary operations on Hilbert spaces. This method is motivated by recent progress on quantum computing. This new approach leads to much simpler proofs for such genre of bounds on the weight distributions of certain classes of codes. Moreover, in some cases, our bounds are improvements on the earlier bounds. These improvements are achieved, either by extending the range of the weights over which the bounds apply, or by extending the class of codes subjected to these bounds.
distributions of shortened cyclic codes
, 2007
"... Groebner basis techniques to compute weight ..."
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