Research On Cyclic Codes And Its Decoding Algorithms-Construction Of Binary BCH Codes With Design Distance 11 And Complementation Of Its B-M Iterative Decoding Algorithm

This dissertation mainly studies algebraic theory and iterative decoding algorithms of cyclic codes. Through the description of cyclic codes about roots, a family of narrow primitive binary BCH codes with design distance 11 are studied. Furthermore, the dual codes of the binary BCH codes are also studied. The details are given as follow:(1) The calculating formulas of cyclotomic cosets are studied and extended. Exactly, the calculating formula with the condition of (s,n) = 1 or (s,n) = s are presented;(2) According to the characteristics of BCH codes and Mobius inversion formula, the periodic distributions of the binary BCH codes and the dual codes are presented;(3) Importing the function , the calculating formulas about non-cyclic equivalent classes of the binary BCH codes are presented through M(o|¨)bius inversion formula;(4) The Berlekamp-Massey iterative algorithm for the BCH code with the parameters [31,11, d] (d≥11) are designed and implemented.