Recently the notion on binary codes called Z/sub 4/-linearity was introduced. This notion
explains why Kerdock codes and Delsarte-Goethals codes admit formal duals in spite of their …

We investigate an abstract linear duality model which has as special instances several duality
systems of interest in combinatorial optimization: subspace orthogonality, cone polarity, …

In [4] it was shown, that the weight enumerators of two binary ℤ 4 -linearly dual codes satisfy
the McWilliams identity (ie these codes are formally dual). If we consider an arbitrary Galois …

… The definition and notations will be the same for the Z4duality obtained by using the
standard inner product or the Kronecker inner product and the difference will be clear from the …

… Thus, the overall sign appearing in these formulae indicates a Z4-duality nature of the T-duality.
On the other hand, T-duality is usually designed to act as an Z2-duality [24]. This works …

… Actually, the interest in quaternary codes grew in 1994 when Z4-duality was first applied
to Kerdock codes and Preparata codes in [11]. Let h2(X) E Z2[X] be a primitive polynomial of …

… The overall sign appearing in these formulae indicates a Z4-duality nature of the T-duality.
It … perform the Fourier transform 4 times, called Z4-duality. The same property holds for the …

We give a short survey of the results obtained in the last several decades that develop the
theory of linear codes and polylinear recurrences over finite rings and modules following the …

… This turns out to be also the condition to implement the Z4-duality group at the quantum
level. In fact the generator of Z4 maps Seff(J1,C2) to Seff(J1,C2) + …

Z 2k-linear codes Page 1 Z 2k-linear codes Claude Carlet ∗ , GREYC, Université de Caen,
France Abstract We introduce a generalization to Z2k of the Gray map and generalized …