TY - JOUR
T1 - Estimates of the Distance Distribution of Codes and Designs1 1 Research supported in part by Binational Science Foundation (BSF) under grant 1999099
AU - Ashikhmin, A.
AU - Barg, A.
AU - Litsyn, S.
PY - 2001/4
Y1 - 2001/4
N2 - 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.
AB - 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.
KW - Binomial spectrum
KW - Krawtchouk polynomials
KW - constant weight codes
KW - distance distribution
KW - polynomial method
UR - http://www.scopus.com/inward/record.url?scp=34247163278&partnerID=8YFLogxK
U2 - 10.1016/S1571-0653(04)00152-0
DO - 10.1016/S1571-0653(04)00152-0
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AN - SCOPUS:34247163278
SN - 1571-0653
VL - 6
SP - 4
EP - 14
JO - Electronic Notes in Discrete Mathematics
JF - Electronic Notes in Discrete Mathematics
ER -