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Dual product constructions of Reed - Muller type codes (Corresp.)

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Various linear and nonlinear R(r,m) codes having parameters (2^{m}, 2^{k}, 2^{m-r}) with k=\sum _{i=0}^{r}\left(^{m}_{i}\right) are constructed from R(r,q) and R(r,p) codes, m=p+q . A dual construction for R(m-r,m) codes from R(p-r,p) and R(q-r,q) codes is also presented, m=p+q . As a simple corollary we have that the number of nonequivalent R(r,m) codes is at least exponential in the length (for r> 1) . For R(m-r,m) codes, the lower bound is doubly exponential in the length (for r> 1) .

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Information Theory, IEEE Transactions on  (Volume:32 ,  Issue: 1 )