1. A speech coder using an orthogonal search, by calculating a term of a search reference value, the speech coder comprising: an adaptive codebook that generates an adaptive codevector representing a pitch component; a random codebook that generates a random codevector representing a random component; a synthesis filter that generates a synthetic speech signal by the synthesis filter being excited by the adaptive codevector and the random codevector; and a distortion calculator that calculates a distortion between an input speech signal and the synthetic speech signal, and selects one random codevector that minimizes the distortion, wherein the distortion calculator calculating the term comprises: a system that computes the power, p t H t Hp, of a signal, Hp, obtained by synthesis in the synthesis filter using the adaptive codevector, computes an auto-correlation matrix, H t H, of filter coefficients of the synthesis filter and calculates a first matrix, N=(p t H t Hp)H t H, by multiplying each element of the auto-correlation matrix by the power; a system that calculates a second matrix, M, by providing a time reverse synthesis, r t =p t H t H, to the signal, Hp, obtained by syntheses in the synthesis filter using the adaptive codevector and by taking an outer product, M=rr t , of the resultant signal by the time reverse synthesis; a system that calculates a third matrix, L=N−M, by using the first matrix and the second matrix; and a system that calculates the term with reference to the third matrix, and wherein p is the adaptive codevector, H is the synthesis filter coefficient matrix, and t denotes transpose.