We study the geometrical properties of the subgroups of the mutliplicative group of a "nite extension of a "nite "eld endowed with its vector space structure and we show that in some cases the associated projective space has a natural group structure. We construct some cyclic codes related to Reed}Muller codes by evaluating polynomials on these subgroups. The geometrical properties of these gro...

A novel onset based optimization method is proposed to convert a Fixed Polarity Reed-Muller (FPRM) function to a compact Multi-level Mixed Polarity Reed-Muller (MMPRM) forms. Onset table is introduced to represent an FPRM function. By operating on the onset table to extract common variables, its compact MMPRM is obtained. The spatial complexity of the proposed algorithm is O(M×n) (M is onset si...

3 Submitted to JGR 4 The Third Santa Fe Conference on Global and Regional Climate Change 5 Manuscript # 2012JD018202 6 7 8 Robert Rohde, Richard A. Muller, Robert Jacobsen, 9 Elizabeth Muller, Saul Perlmutter, Arthur Rosenfeld, 10 Jonathan Wurtele,Donald Groom, Charlotte Wickham 11 12 Corresponding Author Address: 13 Richard A. Muller 14 Berkeley Earth Project 15 2831 Garber St. 16 Berkeley CA...

OFDM, power, Reed-Muller code, decoding, algorithms, error correction Recently a class of generalised Reed-Muller codes has been suggested for use in power-controlled OFDM modulation. A number of approaches to decoding these codes have already been developed. Here we present low complexity alternatives which are inspired by the classical Reed decoding algorithm for binary Reed-Muller codes. We ...

The approach to error correction coding taken by modern digital communication systems started in the late 1940’s with the ground breaking work of Shannon, Hamming and Golay. ReedMuller (RM) codes were an important step beyond the Hamming and Golay codes because they allowed more flexibility in the size of the code word and the number of correctable errors per code word. Whereas the Hamming and ...

R~sum~. On inlroduit une classe de codes lintaires de la famille des codes de Reed-Muller, les codes de Reed-Muller projectifs. Ces codes sont des extensions des codes de Reed-Muller gtntralists ; les codes de Reed-Muller projectifs d'ordre I atteignent la borne de Plotkin. On donne les traram&res des codes de Reed-Muller projecfifs d'ordre 2. 1.Introduction We note pm(Fq) the projective space ...

Muller games are played by two players moving a token along a graph; the winner is determined by the set of vertices that occur infinitely often. The central algorithmic problem is to compute the winning regions for the players. Different classes and representations of Muller games lead to problems of varying computational complexity. One such class are parity games; these are of particular sig...

We investigate weighted finite state automata with the Büchi-acceptance condition. The costs of computations depend on the state of the computation and on the time when it is executed. We characterize those systems whose behaviour is continuous. Then we introduce weighted Muller-automata and show that their behaviour is even Lipschitz-continuous. Under some not to hard restrictions we show that...

A set of quantum error correcting codes based on classical Reed-Muller codes is described. The codes have parameters [[n, k, d]] = [[2r, 2r −C(r, t)− 2 ∑t−1 i=0 C(r, i), 2 t + 2t−1]]. The study of quantum information is currently stimulating much interest. Most of the basic concepts of classical information theory have counterparts in quantum information theory, and among these is the idea of a...

I investigate the structure of an argument that culture cannot be maintained in a population if each individual acquires a given cultural variant from a single person. I note two puzzling consequences of the argument: It appears to conflict with (a) many models of cultural transmission and (b) real-world cases of cultural transmission. I resolve the first puzzle by showing that one of the model...