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Triple-error-correcting

1.        Obtain the generator polynomial of the triple-error-correcting BCH code. Use GF (25) which is constructed using the primitive polynomial p(x) = x5 + x3 + 1. 2.       Find the generator and parity check matrices of the double-error-correcting BCH code obtained using GF(24). Use p(x) = x4 + x3 + 1 for the construction of GF (24).

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Cyclic code

1.        The generator polynomial of the double-error-correcting BCH(15, 7) cyclic code is given as g (x) = x8 + x7 + x6 + x4 + 1: The data-word polynomial is d(x) = x6 + x3 + x + 1. Obtain the systematic and non-systematic code-words for d(x). 2.        For any triple-error-correcting BCH code, find the coefficients of error location polynomial in terms

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Primitive polynomial

1. The generator polynomial of the double-error-correcting Reed-Solomon code RS (7, 3) over GF(23), constructed using the primitive polynomial p(x) . x3 + x + 1, can be calculated as g(x) = x4 + α3 x3 + x2 + αx + α3: The data-word polynomial is given as d(x) = α3 x2 + α2 x + α4. Systematically encode d(x).

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Data vector

1.       The extended field GF(23) is generated using the primitive polynomial p(x) = x3 + x2 + 1. Find the generator polynomial of the single-error-correcting Reed-Solomon code over GF(23). 2.        Express the data vector d . [α3 0 α4 α5 α2] in bit vector form. The elements of the data vector are chosen from GF(23) which is constructed using the

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Extended field

The triple-error-correcting BCH(15, 5) code is constructed on the extended field GF(24). The extended field GF(24) is obtained using the primitive polynomial p (x) = x4 + x3 + 1. The data-word polynomial is d(x) . x6 + x3 + x + 1. Assume that a data-word is encoded and the generated code-word c(x) is transmitted. The received word at the receiver

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