Spectral Orbits and Peak-to-Average Power Ratio of Boolean Functions with respect to the {I,H,N}^n Transform

We enumerate the inequivalent self-dual additive codes over GF(4) of blocklength n, thereby extending the sequence A090899 in The On-Line Encyclopedia of Integer Sequences from n = 9 to n = 12. These codes have a well-known interpretation as quantum codes. They can also be represented by graphs, where a simple graph operation generates the orbits of equivalent codes. We highlight the regularity and structure of some graphs that correspond to codes with high distance. The codes can also be interpreted as quadratic Boolean functions, where inequivalence takes on a spectral meaning. In this context we define PAR_IHN, peak-to-average power ratio with respect to the {I,H,N}^n transform set. We prove that PAR_IHN of a Boolean function is equivalent to the the size of the maximum independent set over the associated orbit of graphs. Finally we propose a construction technique to generate Boolean functions with low PAR_IHN and algebraic degree higher than 2.Comment: Presented at Sequences and Their Applications, SETA'04, Seoul, South Korea, October 2004. 17 pages, 10 figure

Directed Graph Representation of Half-Rate Additive Codes over GF(4)

We show that (n,2^n) additive codes over GF(4) can be represented as directed graphs. This generalizes earlier results on self-dual additive codes over GF(4), which correspond to undirected graphs. Graph representation reduces the complexity of code classification, and enables us to classify additive (n,2^n) codes over GF(4) of length up to 7. From this we also derive classifications of isodual and formally self-dual codes. We introduce new constructions of circulant and bordered circulant directed graph codes, and show that these codes will always be isodual. A computer search of all such codes of length up to 26 reveals that these constructions produce many codes of high minimum distance. In particular, we find new near-extremal formally self-dual codes of length 11 and 13, and isodual codes of length 24, 25, and 26 with better minimum distance than the best known self-dual codes.Comment: Presented at International Workshop on Coding and Cryptography (WCC 2009), 10-15 May 2009, Ullensvang, Norway. (14 pages, 2 figures

What causes hidradenitis suppurativa ?—15 years after

The 14 authors of the first review article on hidradenitis suppurativa (HS) pathogenesis published 2008 in EXPERIMENTAL DERMATOLOGY cumulating from the 1st International Hidradenitis Suppurativa Research Symposium held March 30–April 2, 2006 in Dessau, Germany with 33 participants were prophetic when they wrote “Hopefully, this heralds a welcome new tradition: to get to the molecular heart of HS pathogenesis, which can only be achieved by a renaissance of solid basic HS research, as the key to developing more effective HS therapy.” (Kurzen et al. What causes hidradenitis suppurativa? Exp Dermatol 2008;17:455). Fifteen years later, th

Rate-1/2 component codes for nonbinary turbo codes

INSPEC Accession Number:8584465 DOI: 10.1109/TCOMM.2005.855019The iterative decoding structure and component maximum a posteriori decoders used for decoding binary concatenated codes can be extended to the nonbinary domain. This paper considers turbo codes over nonbinary rings, specifically ternary, quaternary, penternary, hexernary, and octernary codes. The best rate-1/2 component codes are determined using a practical search algorithm. The performance of the resulting rate-1/3 turbo codes on an additive white Gaussian noise channel using q-ary phase-shift keying modulation is given

A method for the analysis of diversity combining for the detection of FH synchronization probes

The authors demonstrate an analysis method for finding the probability of detection of a synchronization probe burst when time diversity is employed. They introduce an analytical approach that is capable of determining the performance of a number of diversity-combining algorithms. The analysis uses circularly symmetric function theory, Fourier-Bessel series, and Fourier series. Examples show the calculation of probability of detector for two threshold schemes in the presence of broadband noise, and in the presence of broadband noise with broadband tone jamming

Unified approach to time diversity combining for fast frequency hopped NCMFSK-anti-jam processing

Frequency hopping (FH) spread spectrum is used in communications systems to provide protection against jamming. With fast FH, there are L ≥ 1 hops per data symbol transmitted. In the presence of severe interference, additional protection can be obtained by processing the LM values obtained from the demodulator. This processing is termed diversity combining. Many powerful and robust types of diversity combining have been developed to reduce the effects of a large jamming signal on some of the L hops. In this paper, a survey of combining methods is presented. Simulation performance results are given for severe noise and multitone jamming (SJR = 0.0 dB). It is found that bit error rates as high as 0.4 can be reduced to < 0.1 for L < 10 using any of sev