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Algebraic Coding - Math Tripos - Past Exam

Exams, Mathematics

Post: February 28th, 2013
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This is the Past Exam of Math Tripos which includes Category Theory, Black Holes, Klein-Gordon Equation, Banach Algebras, Astrophysical Fluid Dynamics etc. Key important points are: Algebraic Coding, Reed–Solomon Codes, Generator Polynomial, Primitive Element, Field Table, Binary Linear Code, Generating Matrix, Binary Hamming Code of Length, Contribution From, Mac Williams Identity
This is the Past Exam of Math Tripos which includes Category Theory, Black Holes, Klein-Gordon Equation, Banach Algebras, Astrophysical Fluid Dynamics etc. Key important points are: Algebraic Coding, Reed–Solomon Codes, Generator Polynomial, Primitive Element, Field Table, Binary Linear Code, Generating Matrix, Binary Hamming Code of Length, Contribution From, Mac Williams Identity
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MATHEMATICAL TRIPOS Monday 3 June 2002 1.30 to 3.30 Part III PAPER 30 ALGEBRAIC CODING Attempt THREE questions There are three questions in total The questions carry equal weight Candidates may bring into the examination any lecture notes made during the course, printed lecture notes, example sheets and model solutions, and books or their photocopies You may not start to read the questions printed on the subsequent pages until instructed to do so by the Invigilator. 2 1 Define Reed–Solomon codes and prove that they are maximum distance separable. Prove that the dual of a Reed–Solomon code is a Reed–Solomon code. Find the minimum distance of a Reed–Solomon code of length 15 and rank 11 and the generator polynomial g1 (X ) over F16 for this code. Use the provided F16 field table to write g1 (X ) in the form ω i0 + ω i1 X + ω i2 X 2 + . . ., identifying each coefficient as a single power of a primitive element ω of F16 . Find the generator polynomial g2 (X ) and the mi..

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