Optimal context quantizers for minimum conditional entropy can be constructed by dynamic programming in the probability simplex space. The main difficulty, operationally, is the resulting complex quantizer mapping function in the context space, in which the conditional entropy coding is conducted. To overcome this difficulty, we propose new algorithms for designing context quantizers in the context space based on the multiclass Fisher discriminant and the kernel Fisher discriminant (KFD). In particular, the KFD can describe linearly nonseparable quantizer cells by projecting input context vectors onto a high-dimensional curve, in which these cells become better separable. The new algorithms outperform the previous linear Fisher discriminant method for context quantization. They approach the minimum empirical conditional entropy context quantizer designed in the probability simplex space, but with a practical implementation that employs a simple scalar quantizer mapping function rather than a large lookup table.