Remarks on the k-error linear complexity of p(n)-periodic sequences

Recently the first author presented exact formulas for the number of 2ⁿn-periodic binary sequences with given 1-error linear complexity, and an exact formula for the expected 1-error linear complexity and upper and lower bounds for the expected k-error linear complexity, k >2, of a random 2ⁿn-periodic binary sequence. A crucial role for the analysis played the Chan-Games algorithm. We use a more sophisticated generalization of the Chan-Games algorithm by Ding et al. to obtain exact formulas for the counting function and the expected value for the 1-error linear complexity for pⁿn-periodic sequences over Fp, p prime. Additionally we discuss the calculation of lower and upper bounds on the k-error linear complexity of pⁿn-periodic sequences over Fp

An iterative algorithm for parametrization of shortest length shift registers over finite rings

The construction of shortest feedback shift registers for a finite sequence S_1,...,S_N is considered over the finite ring Z_{p^r}. A novel algorithm is presented that yields a parametrization of all shortest feedback shift registers for the sequence of numbers S_1,...,S_N, thus solving an open problem in the literature. The algorithm iteratively processes each number, starting with S_1, and constructs at each step a particular type of minimal Gr\"obner basis. The construction involves a simple update rule at each step which leads to computational efficiency. It is shown that the algorithm simultaneously computes a similar parametrization for the reciprocal sequence S_N,...,S_1.Comment: Submitte

The asymptotic behavior of the joint linear complexity profile of multisequences

10.1007/s00605-005-0392-2Monatshefte fur Mathematik1502141-15

Response of Invertebrate Assemblages to Phragmites Australis Invasion and Native Plant Revegetation in Great Salt Lake Wetlands

An invasive grass, Phragmites australis (common reed), is rapidly invading wetlands surrounding the Great Salt Lake in Utah, outcompeting native vegetation, and substantially altering critical habitat for migratory shorebirds and waterfowl. Although the removal of Phragmites can help restore native vegetation, additional factors, such as food resource availability, contribute to bird habitat quality. Specifically, invertebrates provide an important food source for many bird species, yet how Phragmites may be altering invertebrate assemblages is unclear. This project addresses three primary objectives to fill these knowledge gaps: 1) examine how invertebrate assemblages respond to Phragmites invasion 2) identify if Phragmites removal and the reestablishment of native vegetation can restore invertebrate species composition, biomass, and diversity within previously invaded wetlands and 3) estimate the role of different restoration techniques in determining invertebrate recovery success. To accomplish these objectives, we are examining the invertebrate assemblages associated with dominant native wetland vegetation types, areas invaded by Phragmites, and active restoration sites using a combination of emergence and flight-intercept traps. Our results indicate that there may be specific habitat types that are more valuable to developing aquatic insect larvae than other areas. Furthermore, our samples also suggest a difference in terrestrial invertebrate activity between Phragmites and native vegetation areas. Recognizing how invertebrates interact with Phragmites and native vegetation is a critical component of understanding how to restore these wetland habitats for birds. By gaining a better understanding of these relationships, invertebrate assemblage composition could serve as a potential assessment metric for determining wetland restoration success