We study certain projections of binary linear codes onto larger fields. These projections include the well-known projection of the extended Golay [24, 12, 8] code onto the Hexacode over GF(4) and the projection of the Reed-Muller code R(2, 5) onto the unique self-dual [8, 4, 4] code over GF(4). We give a characterization of these projections, and we construct several binary linear codes which h...

Neuroscientists formulate very different hypotheses about the nature of neural code. At one extreme, it has been argued that neurons encode information in relatively slow changes of individual spikes arriving rates (rates codes) and the irregularity in the spike trains reflects noise in the system, while in the other extreme this irregularity is the code itself (temporal codes) thus the precise...

Many experts believe that new malware is created at a rate faster than legitimate software. For example, in 2007 over one million new malware samples were collected by a major security solution vendor. However, it is often speculated, though to the best of our knowledge unproven, that new malware is produced by modifying existing malware, either through simple tweaks, code composition, or a var...

A family of neuromorphic networks specifically designed for communications and optical signal processing applications is presented. The information is encoded utilizing sparse Optical Orthogonal Code sequences on the basis of unipolar, binary (0,1) signals. The generalized synaptic connectivity matrix is also unipolar, and clipped to binary (0,1) values. In addition to high-capacity associative...

In the paper we show the existence of a large class of extended perfect binary codes containing maximum ij-components.

Let x ∈ R be given. As we know the, amount of bits needed to binary code x with given accuracy (h ∈ R) is approximately mh(x) ≈ log2(max{1, | h |}). We consider the problem where we should translate the origin a so that the mean amount of bits needed to code randomly chosen element from a realization of a random variable X is minimal. In other words, we want to find a ∈ R such that R 3 a→ E(mh(...

An elementary construction using binary codes gives new record kissing numbers in dimensions from 32 to 128.

We give six improved bounds on A(n, d, w), the maximum cardinality of a binary code of length n with minimum distance d and constant weight w.

We present a construction of 1-perfect binary codes, which gives a new lower bound on the number of such codes. We conjecture that this lower bound is asymptotically tight.

It is proven that for any numbers n = 2 m − 1, m ≥ 4 and r, such that n − log(n + 1) ≤ r ≤ n excluding n = r = 63, n = 127, r ∈ {126, 127} and n = r = 2047 there exists a propelinear perfect binary code of length n and rank r.