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...

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...

Given an arbitrary n, we consider anisotropic quadratic forms of dimension n over all fields of characteristic = 2 and prove that the height of an n-dimensional excellent form (depending on n only) is the (precise) lower bound of the heights of all forms of dimension n.

a trial study was carried out to assess the influence of the plant residue management in conjuction with application of different nitrogen sources on wheat yield and components, at the agricultural faculty of shahidchamran university of ahvaz during 2011-2012.the experimental design was splitplot at randomized completed block design arrangement. the main plot were different wheat residue manage...

background: tetracyclines (tcs) are broad-spectrumantibiotics that are widely used in veterinary medicine. thepresence of tcs residues in milk is a public health concern allover the world. objectives:this study aimed to determine tcsresiduals in pasteurized milk marketed by some dairy companiesin tehran from april 2011 to march 2012. methods: 432pasteurized milk samples were purchased from supe...

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