NONBINARY DELSARTE–GOETHALS CODES AND FINITE SEMIFIELDS

Symplectic finite semifields can be used to construct nonlinear binary codes of Kerdock type (i.e., with the same parameters of the Kerdock codes, a subclass of Delsarte–Goethals codes). In this paper, we introduce nonbinary Delsarte–Goethals codes of parameters $(q^{m+1}\ ,\ q^{m(r+2)+2}\ ,\ {\frac{q-1}{q}(q^{m+1}-q^{\frac{m+1}{2}+r})})$ over a Galois field of order $q=2^l$ , for all $0\le r\le\frac{m-1}{2}$ , with m ≥ 3 odd, and show the connection of this construction to finite semifields.

Beamforming with Kerdock Codes in LTE System for High-Speed Railway

Beamforming technique based the reciprocity of LTE communication system for high-speed railway is a practical way to improve the system performance in this paper. Kerdock codes, which facilitate efficient codebook and codeword search, are implemented in the LTE system for high-speed railway as the beamforming precoding codebook. The analysis of complexity and simulation results about the communication system of the beamforming with Kerdock codes (KBF) show that the proposed KBF can eliminate complex multiplications and improve the Bit Error Rate (BER) performance at large SNR compared with the existing beamfoming communication system for high-speed railway.