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- W2046266410 abstract "A code over GF(q <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>m</sup> ) can be imaged or expanded into a code over GF(q) using a basis for the extension field over the base field. In this work, a generalized version of the problem of self-orthogonality of the q-ary image of a q <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>m</sup> -ary code has been considered. Given an inner product (more generally, a biadditive form), necessary and sufficient conditions have been derived for a code over a field extension and an expansion basis so that an image of that code is self-orthogonal. The conditions require that the original code be self-orthogonal with respect to several related biadditive forms whenever certain power sums of the dual basis elements do not vanish. The conditions are particularly simple to state and apply for cyclic codes. As a possible application, new quantum error-correcting codes have been constructed with larger minimum distance than previously known." @default.
- W2046266410 created "2016-06-24" @default.
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- W2046266410 date "2007-06-01" @default.
- W2046266410 modified "2023-09-27" @default.
- W2046266410 title "Self-orthogonality of Images and Traces of Codes with Applications to Quantum Codes" @default.
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- W2046266410 doi "https://doi.org/10.1109/isit.2007.4557237" @default.
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