A brief survey on low weight codewords of generalized Reed-Muller codes and projective generalized Reed-Muller codes is presented. In the affine case some information about the words that reach the second distance is given. Moreover the second weight of the projective Reed-Muller codes is estimated, namely a lower bound and an upper bound of this weight are given.

A formula, which relates the state dimensions of a minimal trellis of a Reed-Muller code to those of another Reed-Muller code with lower order and shorter length, is derived in this correspondence. State dimension at every position of a minimal trellis of any Reed-Muller code can be obtained by a recursive application of this formula.

This paper presents a design method of easily testable AND-EXOR networks. It is an improvement of Reddy and SalujaReddy’s methods, and has the following features: 1) The network uses generalized Reed-Muller expressions (GRMs) instead of Positive Polarity Reed-Muller expressions (PPRMs). The average number of products for GRMs is less than half of that for PPRMs, and is less than that of sum-of-...

It is proved a generalization of Cusick-Cheon’s conjecture on balanced Boolean functions in the cosets of the binary Reed-Muller code RM (k ,m) of order k and length 2m, when k = 1 or k ≥ (m − 1)/2.

This paper extends and confirms the report of Calabrese (Calabrese, E. J. (2011b). Muller's Nobel Lecture on dose-response for ionizing radiation: Ideology or science? Arch. Toxicol. 85, 1495-1498) that Hermann J. Muller knowingly made deceptive comments in his 1946 Nobel Prize Lecture (Muller, H. J. (1946). Nobel Prize Lecture. Stockholm, Sweden. Available at http://www.nobelprize.org/. Access...

Gopalan, Klivans, and Zuckerman proposed a list-decoding algorithm for Reed-Muller codes. Their algorithm works up to a given list-decoding radius. Dumer, Kabatiansky, and Tavernier improved the complexity of the algorithm for binary Reed-Muller codes by using wellknown Plotkin construction. In this study, we propose a list-decoding algorithm for non-binary Reed-Muller codes as a natural genera...

Muller cells, the principal glia of the retina, play several key roles in normal and various retinal diseases. To date, their direct involvement in retinal innate defense against bacterial pathogens has not been investigated. In this article, we show that Muller cells express TLR2, a key sensor implicated in recognizing Gram-positive bacteria. We found that intravitreal injection of TLR2 agonis...

PURPOSE To investigate the expression of RDH10, an all-trans retinol dehydrogenase identified in the retinal pigment epithelium (RPE), in retinal Muller cells. METHODS The RDH10 protein levels in mouse eyecups and bovine tissues were examined by Western blot analysis using a polyclonal antibody against RDH10. The cellular localization in the retina was determined by immunohistochemistry. Expr...