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

How to determine linear complexity and kk-error linear complexity in some classes of linear recurring sequences

Several fast algorithms for the determination of the linear complexity of $d$-periodic sequences over a finite field \F_q, i.e. sequences with characteristic polynomial $f(x) = x^d-1$, have been proposed in the literature. In this contribution fast algorithms for determining the linear complexity of binary sequences with characteristic polynomial $f(x) = (x-1)^d$ for an arbitrary positive integer $d$, and $f(x) = (x^2+x+1)^{2^v}$ are presented. The result is then utilized to establish a fast algorithm for determining the $k$-error linear complexity of binary sequences with characteristic polynomial $(x^2+x+1)^{2^v}$

Ensembl 2005

The Ensembl (http://www.ensembl.org/) project provides a comprehensive and integrated source of annotation of large genome sequences. Over the last year the number of genomes available from the Ensembl site has increased by 7 to 16, with the addition of the six vertebrate genomes of chimpanzee, dog, cow, chicken, tetraodon and frog and the insect genome of honeybee. The majority have been annotated automatically using the Ensembl gene build system, showing its flexibility to reliably annotate a wide variety of genomes. With the increased number of vertebrate genomes, the comparative analysis provided to users has been greatly improved, with new website interfaces allowing annotation of different genomes to be directly compared. The Ensembl software system is being increasingly widely reused in different projects showing the benefits of a completely open approach to software development and distribution

Global patterns in endemicity and vulnerability of soil fungi

Fungi are highly diverse organisms, which provide multiple ecosystem services. However, compared with charismatic animals and plants, the distribution patterns and conservation needs of fungi have been little explored. Here, we examined endemicity patterns, global change vulnerability and conservation priority areas for functional groups of soil fungi based on six global surveys using a high-resolution, long-read metabarcoding approach. We found that the endemicity of all fungi and most functional groups peaks in tropical habitats, including Amazonia, Yucatan, West-Central Africa, Sri Lanka, and New Caledonia, with a negligible island effect compared with plants and animals. We also found that fungi are predominantly vulnerable to drought, heat and land-cover change, particularly in dry tropical regions with high human population density. Fungal conservation areas of highest priority include herbaceous wetlands, tropical forests, and woodlands. We stress that more attention should be focused on the conservation of fungi, especially root symbiotic arbuscular mycorrhizal and ectomycorrhizal fungi in tropical regions as well as unicellular early-diverging groups and macrofungi in general. Given the low overlap between the endemicity of fungi and macroorganisms, but high conservation needs in both groups, detailed analyses on distribution and conservation requirements are warranted for other microorganisms and soil organisms

Global patterns in endemicity and vulnerability of soil fungi

Fungi are highly diverse organisms, which provide multiple ecosystem services. However, compared with charismatic animals and plants, the distribution patterns and conservation needs of fungi have been little explored. Here, we examined endemicity patterns, global change vulnerability and conservation priority areas for functional groups of soil fungi based on six global surveys using a high-resolution, long-read metabarcoding approach. We found that the endemicity of all fungi and most functional groups peaks in tropical habitats, including Amazonia, Yucatan, West-Central Africa, Sri Lanka, and New Caledonia, with a negligible island effect compared with plants and animals. We also found that fungi are predominantly vulnerable to drought, heat and land-cover change, particularly in dry tropical regions with high human population density. Fungal conservation areas of highest priority include herbaceous wetlands, tropical forests, and woodlands. We stress that more attention should be focused on the conservation of fungi, especially root symbiotic arbuscular mycorrhizal and ectomycorrhizal fungi in tropical regions as well as unicellular early-diverging groups and macrofungi in general. Given the low overlap between the endemicity of fungi and macroorganisms, but high conservation needs in both groups, detailed analyses on distribution and conservation requirements are warranted for other microorganisms and soil organisms

How many bits have to be changed to decrease the linear complexity?

10.1023/B:DESI.0000035466.28660.e9Designs, Codes, and Cryptography332109-122DCCR

Periodic sequences with maximal linear complexity and large k-error linear complexity

10.1007/s00200-003-0134-4Applicable Algebra in Engineering, Communications and Computing144273-286AAEC

On the expected value of the linear complexity and the κ-error linear complexity of periodic sequences

10.1109/TIT.2002.804050IEEE Transactions on Information Theory48112817-2825IETT