Difference Sets in Z_4^m and F_2^2m
Designs, Codes and Cryptography
Finite Commutative Rings and Their Applications
Finite Commutative Rings and Their Applications
Trace-Function on a Galois Ring in Coding Theory
AAECC-12 Proceedings of the 12th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Z8-Kerdock codes and pseudorandom binary sequences
Journal of Complexity - Special issue on coding and cryptography
More correlation-immune and resilient functions over Galois fields and Galois rings
EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques
The Z4-linearity of Kerdock, Preparata, Goethals, and related codes
IEEE Transactions on Information Theory
Constructions of Low Rank Relative Difference Sets in 2-Groups Using Galois Rings
Finite Fields and Their Applications
New Partial Difference Sets in Ztp2 and a Related Problem about Galois Rings
Finite Fields and Their Applications
Symmetric bilinear forms over finite fields of even characteristic
Journal of Combinatorial Theory Series A
Witt index for Galois Ring valued quadratic forms
Finite Fields and Their Applications
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We introduce an invariant for nonsingular quadratic forms that take values in a Galois Ring of characteristic 4. This notion extends the invariant in Z"8 for Z"4-valued quadratic forms defined by Brown [E.H. Brown, Generalizations of the Kervaire invariant, Ann. of Math. (2) 95 (2) (1972) 368-383] and studied by Wood [J.A. Wood, Witt's extension theorem for mod four valued quadratic forms, Trans. Amer. Math. Soc. 336 (1) (1993) 445-461]. It is defined in the associated Galois Ring of characteristic 8. Nonsingular quadratic forms are characterized by their invariant and the type of the associated bilinear form (alternating or not).