Professor C.F.J. Muller as historikus

Professor Simon Newcomb as an Astronomer.

MSS. intended for publication and books, etc., intended for review should be sent to the Editor of SCIENCE, Garrison-onHudson, N. Y. PROIFESSOR SIMON NEWCOMB AS AN ASTRONOMER PROFESSOR NEWCOMB has narrated at considerable length the personal incidents of his scientific career in his book "The Reminiscences of an Astronomer," and to that source the reader desirousi of knowing them may be referre...

Minimum-weight codewords as generators of generalized Reed-Muller codes

We establish the range of values of ρ, where 0 ≤ ρ ≤ m(q − 1), for which the generalized Reed-Muller code RFq (ρ,m) of length q over the field Fq of order q is spanned by its minimum-weight vectors.

Minimum-weight odewords as generators of generalized Reed-Muller odes

Quantum Reed-Muller Codes

This paper presents a set of quantum Reed-Muller codes which are typically 100 times more effective than existing quantum Reed-Muller codes. The code parameters are [[n, k, d]] = [[2, ∑r l=0 C(m, l) − ∑m−r−1 l=0 C(m, l), 2 m−r ]] where 2r + 1 > m > r.

Generalized Reed-Muller Codes

the possible choices for n and k are rather thinly distributed in the class of all pairs (n, k) with k ~ n--and it is, therefore, often inefficient to make use of such codes in concrete situations (that is, when a desired pair (n, k) is far from any achievable pair). We have succeeded in overcoming this difficulty by generalizing the Reed-Muller codes in such a way that they exist for every pai...