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A new approach to error-correcting codes

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A correspondence between linear(n,k,d)codes and algorithms for computing a systempsiofkbilinear forms is established under which the codelengthnis equal to the multiplicative complexity of the algorithm for computingpsi, and the code distancedis underbounded by the minimum number of multiplications required to compute any linear combination of thekforms inpsi. This hitherto unexplored approach to linear codes holds promise of a better understanding of the structure of existing codes as well as for methods of constructing new codes with prescribed rate and distance.

Published in:

Information Theory, IEEE Transactions on  (Volume:23 ,  Issue: 4 )

Date of Publication:

Jul 1977

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