New Synthesis of Even-cell 90/150 MWCA
Un-Sook Choi, Sung-Jin Cho, Han-Doo Kim and Sung-Won Kang
Reversible codes are advantageous in certain data storage systems that can read data in bi-direction. Self-reciprocal polynomials are applied to the design of reversible error-correcting codes with read-backward properties and to the efficient implementation of linear feedback shift registers(LFSRs). In this paper, we propose a method to determine whether a self-reciprocal polynomial f2n(x)(n ∈ 𝐍) with maximum weight is a CA-polynomial or not. By the proposed method we can construct 2n-cell 90/150 MWCA with only (n − 1)-cell transition rules when f2n(x) is a CA-polynomial by using a symmetric transition rule block and the small transition rule block < 0, 1 >. Also, we give an efficient 90/150MWCA synthesis algorithm for the CA-polynomial f2n (x) using the proposed method. This algorithm is an improvement of the algorithm (SynthesisOfLHGCA) proposed by Cho et al.  for the CApolynomial f2n(x).
Keywords: Maximum weight polynomial, self-reciprocal polynomial, rule block, CA-polynomial, reversible code, MWCA