ABSTRACT
Certain preliminaries needed for the study of linear codes are given. In particular, the binary symmetric channel, block codes and linear codes of length n over https://www.w3.org/1998/Math/MathML"> F https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781351023344/b6c68d68-1226-4347-aaa8-58dfe0c0d0a9/content/eq1968.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> q , a finite field having q = pm, p a prime; m ≥ 1, are briefly, described. An account of the properties of cyclic codes of length n over https://www.w3.org/1998/Math/MathML"> F https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781351023344/b6c68d68-1226-4347-aaa8-58dfe0c0d0a9/content/eq1969.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> q is presented. The role of q-cyclotomic cosets modulo n is pointed out. A few theorems due to Carry Huffman and Vera Pless [ 6 ] are given with proofs.
