On this page, the properties of Galois fields GF(2 m) based on primitive polynomials of degree m are used to create a generating matrix for cyclic block codes.Ī Galois field GF(2 3) = GF(8) specified by the primitive polynomial P(x)=(1011) of degree 3 serves to define a generator matrix G(x) to create a set of (7,4) codewords for single-bit error correction (D=3). 1 Introduction When a digital shift register of N bit length ( g. The a i 20 1 are parameters which a ect the properties of the circuit. The circles with ’+’ signs denote exclusive-or gates. ECE4253 Code Generation with Galois Fieldsĭepartment of Electrical and Computer Engineering - University of New Brunswick, Fredericton, NB, Canada Implementing a shift register into a Matlab. Figure 1: ‘Fibonacci’ type linear shift register with exclusive-or feedback and input sig-nal.
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