It is shown that the extended quadratic residue code of length 20 over GF(7) is a unique self-dual [20, 10, 9] code C such that the lattice obtained from C by Construction A is isomorphic to the 20-dimensional unimodular lattice D 20, up to equivalence. This is done by converting the classification of such self-dual codes to that of skew-Hadamard matrices of order 20.

The largest minimum weight of a self-dual doubly-even binary (n, k, d) code is d = 4bn/24c+ 4. Of such codes with length divisible by 24, the Golay Code is the only (24, 12, 8) code, the Extended Quadratic Residue Code is the only known (48, 24, 12) code, and there is no known (72, 36, 16) code. One may partition the search for a (48, 24, 12) self-dual doubly-even code into 3 cases. A previous ...

The toric residue is a map depending on n + 1 divisors on a complete toric variety of dimension n . It appears in a variety of contexts such as sparse polynomial systems, mirror symmetry, and GKZ hypergeometric functions. In this paper we investigate the problem of finding an explicit element whose toric residue is equal to one. Such an element is shown to exist if and only if the associated po...

bacteria play an important role in the initiation and progression of diseases (not only in disease but affect health status of individual). populations of digestive microflora in chicken gut change with age and also affected by diet, stressors, and performance enhancers as well as in disease conditions. the aim of the pre-sent study was to know bacterial makeup in chicken gut, using denaturing ...

In this paper, a decoding method is proposed for the (41, 21, 9) quadratic residue code. The method is acquired through applying the condition of the modified Gao’s algorithm that is similar to fast transform decoding developed by Shiozaki [8]. The property of the syndrome polynomial is used in our decoding method. The new algorithm for has been verified by a software simulation using C languag...

gut microbiota is formed by ten of trillions of microorganisms with at least 1000 different species of known bacteria. one - third of an individual gut microbiota is common to most people, while two - thirds are specific to him. growing amount of evidence indicates that gut microbiota characteristics may play an important role in mental dysfunctions. molecular mimicry between several key neurop...

Gut microbiota is formed by ten of trillions of microorganisms with at least 1000 different species of known bacteria. One - third of an individual gut microbiota is common to most people, while two - thirds are specific to him. Growing amount of evidence indicates that gut microbiota characteristics may play an important role in mental dysfunctions. Molecular mimicry between several key neurop...

alzheimer’s disease (ad) is a neurodegenerative disease that is the most common type of dementia.ad includes 60_80% of dementia and most people with ad have more than 65 years old.ad causes losing neuronal activity by abnormal proteins. plaques of beta-amyloid and tangles of “tau” protein can lead to ad. recently evidence has found that ad may come from outside of central nervous system (cns) a...