In this paper, we consider the Reed-Muller (RM) codes. For the 1st order RM code, we prove that it is unique in the sense that any linear code with the same length, dimension and minimum distance must be the 1st order RM code; For the 2nd order RM code, we give a constructive linear sub-code family for the case when m is even. This is an extension of Corollary 17 of Ch. 15 in the book by MacWil...

I N 1927 H. J. MULLER (1890-1967) published in Science a paper entitled “Artificial Transmutation of the Gene.” It reported the first experimental production of mutations and opened a new era in genetics. The title is curious. Why transmutation rather than mutation? The answer emerges from another paper (MULLER 1928a), written in 1926. After reviewing the repeated failure of efforts by many wor...