## Complete decoding of some binary BCH codes |

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A(a+A affine polynomial affine quartic algorithm for bpBCH(2 Appendix assume knowledge Berlekamp LlJ binary BCH codes binary n-tuple bpBCH(t,m CD-SA/SR channel coding choice code of primitive codes of length codeword of weight coefficients complete decoding algorithm compute Cornell University cosets of weight cyclic shift definition distinct roots elementary symmetric functions elements of GF(2 equation X2 error locator polynomial exist fields of characteristic finite fields given Hartmann irreducible polynomial Jose Antonio Vanderhorst Lemma length shift register linear locator poly locator polynomial corresponding maximal length shift maximum coset weight method minimal polynomial minimum distance Newton's identities parity checks perfect cubes primitive element primitive length PROOF quadratic equation quintic equation received word roots in GF(2m satisfies equations 5.2.4-6 set a(z shift register sequence shown the following solution solve syndrome equal Theorem TR^Lu transformed coset TRLaJ TRLm(A values zero