Title :
Identities and approximations for the weight distribution of q -ary codes
Author :
Cheung, Kar-Ming
Author_Institution :
Jet Propulsion Lab., Pasadena, CA, USA
fDate :
9/1/1990 12:00:00 AM
Abstract :
An explicit formula is derived that enumerates the complete weight distribution of an (n, k, d) linear code using a partially known weight distribution. An approximation formula for the weight distribution of q-ary linear (n, k , d) codes is also derived. It is shown that, for a given q-ary linear (n, k, d) code, the ratio of the number of codewords of weight u to the number of words of weight u approaches the constant Q=q -(n-k) as u becomes large. The error term is a decreasing function of the minimum weight of the dual. The results are also valid for nonlinear (n, M, d) codes with the minimum weight of the dual replaced by the dual distance
Keywords :
error correction codes; (n, k, d) code; approximation formula; codewords; dual distance; linear code; nonlinear (n, M, d) codes; q-ary codes; weight distribution; Algebra; Block codes; Decoding; Error correction codes; Laboratories; Linear code; Propulsion;
Journal_Title :
Information Theory, IEEE Transactions on