Fast computing of the positive polarity Reed - Muller transform over GF ( 2 ) and GF ( 3 )

The problem of efficient computing of binary and ternary positive (or zero) polarity Reed-Muller (PPRM) transform is important for many areas. The matrices, determining these transforms, are defined recursively or by Kronecker product. Using this fact, we apply the dynamic-programming strategy to develop three algorithms. The first of them is a new version of a previous our algorithm for performing the binary PPRM transform. The second one is a bit-wise implementation of the first algorithm. The third one performs the ternary PPRM transform. The last two algorithms have better time complexities in comparison with other algorithms, known to us.