Consider a Galois field GF(23) based on the primitive polynomial h(x) = 1 + x +...

 

 

Transcribed Image Text:

Consider a Galois field GF(23) based on the primitive polynomial h(x) = 1 + x + x. (a) Derive the Galois field based on the given primitive polynomial in terms of binary sequences, polynomial notations and powers of the primitive element (a). (b) Derive the corresponding minimum polynomials. (5 marks) (5 marks) (c) Derive the generator polynomial of a single-error-correcting code based on the min- imum polynomials. What is the rate of the code generated by the derived generator polynomial? (5 marks) (d) If the received sequence is [0 E 10 1 E 0] (E denotes erasure error), determine the codeword that was sent using the syndrome decoding algorithm. (7 marks) Consider a Galois field GF(23) based on the primitive polynomial h(x) = 1 + x + x. (a) Derive the Galois field based on the given primitive polynomial in terms of binary sequences, polynomial notations and powers of the primitive element (a). (b) Derive the corresponding minimum polynomials. (5 marks) (5 marks) (c) Derive the generator polynomial of a single-error-correcting code based on the min- imum polynomials. What is the rate of the code generated by the derived generator polynomial? (5 marks) (d) If the received sequence is [0 E 10 1 E 0] (E denotes erasure error), determine the codeword that was sent using the syndrome decoding algorithm. (7 marks)

Answer rating: 100% (QA)

a To derive the Galois field GF23 based on the primitive polynomial hx 1 x x we first need to repres... View the full answer