Titlebook: Error-Correction Coding and Decoding; Bounds, Codes, Decod Martin Tomlinson,Cen Jung Tjhai,Mubarak Jibril Book‘‘‘‘‘‘‘‘ 2017 The Editor(s) (

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Cyclotomic Cosets, the Mattson–Solomon Polynomial, Idempotents and Cyclic CodesMattson–Solomon polynomial is described and it is shown to be an inverse discrete Fourier transform based on a primitive root of unity. The usefulness of the Mattson–Solomon polynomial in the design of cyclic codes is demonstrated. The relationship between idempotents and the Mattson–Solomon polynom

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Good Binary Linear Codeswith methods and tools for producing new codes which are improvements to currently known codes. The chapter discusses and describes several efficient algorithms for computing the minimum distance and weight distribution of linear codes. Several different methods of constructing codes are described a

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Algebraic Geometry Codesto be asymptotically good. Concepts and notions relevant to AG codes are discussed with particular emphasis laid on the construction of AG codes. A generalised construction of AG codes is introduced and improvements to the tables of best-known codes are presented. This construction utilises the noti

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Analogue BCH Codes and Direct Reduced Echelon Parity Check Matrix Constructionquantisation errors and increases the bandwidth required. The use of analogue error-correcting codes eliminates the need for digitisation. It is shown that analogue BCH codes may be constructed in the same way as finite-field BCH codes, including Reed–Solomon codes, except that the field of complex