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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Witt's extension theorem for mod four valued quadratic forms


Author: Jay A. Wood
Journal: Trans. Amer. Math. Soc. 336 (1993), 445-461
MSC: Primary 11E12; Secondary 15A63, 57R67
MathSciNet review: 1085946
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Abstract: The $ \bmod \,4$ valued quadratic forms defined by E. H. Brown, Jr. are studied. A classification theorem is proven which states that these forms are determined by two things: whether or not their associated bilinear form is alternating, and the $ \sigma $-invariant of Brown (which generalizes the Arf invariant of an ordinary quadratic form). Particular attention is paid to a generalization of Witt's extension theorem for quadratic forms. Some applications to selforthogonal codes are sketched, and an exposition of some unpublished work of E. Prange on Witt's theorem is provided in an appendix.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1993-1085946-7
PII: S 0002-9947(1993)1085946-7
Keywords: Quadratic form, Witt's extension theorem, Witt index, self-orthogonal code, isotropic subspace
Article copyright: © Copyright 1993 American Mathematical Society