A.G. Shanbhag

On the weight hierarchy of Kerdock codes over Z/sub 4/

The rth generalized Hamming weight d/sub r/ of the Kerdock code of length 2/sup m/ over Z/sub 4/ is considered. A lower bound on d/sub r/ is derived for any r, and d/sub r/ is exactly determined for r=0.5, 1, 1.5, 2, 2.5. In the case of length 2/sup 2m/, d/sub r/ is determined for any r, where 0/spl les/r/spl les/m and 2r is an integer. In addition, it is shown that it is sometimes possible to determine the generalized Hamming weights of the Kerdock codes of larger length using the results of d/sub r/ for a given length. The authors also provide a closed-form expression for the Lee weight of a Kerdock codeword in terms of the coefficients in its trace expansion.

Upper bound for a hybrid sum over Galois rings with applications to aperiodic correlation of some q-ary sequences

An upper bound for a hybrid exponential sum over Galois rings is derived. This bound is then used to obtain an upper bound for the maximum aperiodic correlation of some sequence families over Galois rings. The bound is of the order of /spl radic/qlnq where q-1 is the period of the sequences.

Improved estimates via exponential sums for the minimum distance of Z/sub 4/-linear trace codes

An upper hound for Weil-type exponential sums over Galois rings was derived by Kumar, Helleseth, and Calderbank (see ibid., vol.41, no.3, p.456, 1995). This bound leads directly to an estimate for the minimum distance of Z/sub 4/-linear trace codes. An improved minimum-distance estimate is presented. First, McElieces result on the divisibility of the weights of binary cyclic codes is extended to Z/sub 4/ trace codes. The divisibility result is then combined with the techniques of Serre (1983) and of Moreno and Moreno (see ibid., vol.40, no.11, p.1101, 1994) to derive the improved minimum-distance estimate. The improved estimate is tight for the Kerdock code as well as for the Delsarte-Goethals codes.

New codes with the same weight distributions as the Goethals codes and the Delsarte-Goethals codes

AbstractThe Goethals code is a binary nonlinear code of length 2m+1 which has

Electronic signal processing for dispersion compensation and error mitigation in optical transmission networks

\zeta _p

Improved binary codes and sequence families from Z/sub 4/-linear codes

codewords and minimum Hamming distance 8 for any odd

Pre-distortion apparatus

m \geqslant 3