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By using nondegenerate and degenerate quadrics in projective space over finite fields of characteristic 2, some association schemes were constructed and their parameters were computed by the authors (see Adv. in Math., 3(2000), 120-128 and Acta Math. Appl. Sinica, 1 (1999), 96-103). In this note, their polynomial properties,eigenmatrices, imprimitivities, association subschemes and related quotient association schemes are studied.