## Coding Theory |

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Abelian group Barrackpore belong to different Bose close-packed code of length code of level code point Coding Theory columns companion matrix congruence Corollary correcting code corresponding coset G coset leaders cyclic adjacent errors cyclic group code defined Definition denote detection region different cosets divides tn-l divisor efficient burst-correcting code elements of G elements of norm extra digit factor group GF 2m group isomorphic implies Indian Statistical Institute integer Legendre symbol Let G level r+1 matrix of rank maximal group code minimum distance codes mod P(t mod tn-l modulo monic polynomial n,d)-group code non-zero constant term norm preserving number of elements number of points obtained permutation transformation polynomial of degree polynomial P(t positions primitive of degree Proof i Let quadratic residues reduced residue system relatively prime row vectors set of errors t-error correcting n/k)-alphabet Theorem Tp(a unit vectors zero