We propose new results on low weight codewords of affine and projective generalized Reed-Muller codes. In the affine case we give some results on codewords that cannot reach the second weight also called the next to minimal distance. In the projective case the second distance of generalized Reed-Muller codes is estimated, namely a lower bound and an upper bound of this weight are given.

We determine the state complexities of three families of codes that generalise the Reed{Muller codes. Our approach would seem to be new and in particular would seem to provide simpliied proofs of known results on trellises for Reed{Muller codes. One of the families is new and its classical code parameters, which compare well with those of the other codes considered, are given. We conclude with ...

The well known Plotkin construction is, in the current paper, generalized and used to yield new families of Z2Z4-additive codes, whose length, dimension as well as minimum distance are studied. These new constructions enable us to obtain families of Z2Z4-additive codes such that, under the Gray map, the corresponding binary codes have the same parameters and properties as the usual binary linea...

This paper is a survey on the algebraic approach to the theory of automata accepting infinite words. We discuss the various acceptance modes (Büchi automata, Muller automata, transition automata, weak recognition by a finite semigroup, ω-semigroups) and prove their equivalence. We also give two algebraic proofs of McNaughton’s theorem on the equivalence between Büchi and Muller automata. Finall...

After skin wounding, the repair process is initiated by the release of growth factors, cytokines, and bioactive lipids from injured vessels and coagulated platelets. These signal molecules induce synthesis and deposition of a provisional extracellular matrix, as well as fibroblast invasion into and contraction of the wounded area. We previously showed that sphingosine-1-phosphate (S1P) triggers...

BACKGROUND Diabetic retinopathy (DR) is a progressive neurodegenerative disease with early-stage symptoms such as dysfunction of Muller cells, which leads to ganglion cell death. Its pathogenesis is probably associated with oxidative stress and a recently discovered protein, thioredoxin-interacting protein (TXNIP). MATERIAL AND METHODS To explore the role of TXNIP in DR, we cultured Muller cell...

This article provides a novel technique of X (mod P) realization. It is based on the Reed-Muller polynomial expansion. The advantage of the approach concludes in the capability to realize X (mod P) for an arbitrary P. The approach is competitive with the known realizations on the speed processing. Advantages and results of comparison with the known approaches for X [9:1] and P=7 is demonstrated...

We present a structural attack against the Sidelnikov cryptosystem [8]. The attack creates a private key from a given public key. Its running time is subexponential and is effective if the parameters of the Reed-Muller code allow for efficient sampling of minimum weight codewords. For example, the length 2048, 3rd-order Reed-Muller code as proposed in [8] takes roughly an hour to break on a sto...

A variety of diseases lead to degeneration of retinal ganglion cells (RGCs) and their axons within the optic nerve resulting in loss of visual function. Although current therapies may delay RGC loss, they do not restore visual function or completely halt disease progression. Regenerative medicine has recently focused on stem cell therapy for both neuroprotective and regenerative purposes. Howev...