MinT - Information on Result #669631

Information on Result #669631

Linear OA(64⁸⁸, 4179, F₆₄, 35) (dual of [4179, 4091, 36]-code), using (u,Â u+v)-construction based on

linear OA(64¹⁹, 82, F₆₄, 17) (dual of [82, 63, 18]-code), using
- constructionÂ X applied to AG(F,61P) âŠ‚ AG(F,63P) [i] based on
  1. linear OA(64¹⁸, 79, F₆₄, 17) (dual of [79, 61, 18]-code), using algebraic-geometric code AG(F,61P) [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
    - a function field by SÃ©mirat [i]
  2. linear OA(64¹⁶, 79, F₆₄, 15) (dual of [79, 63, 16]-code), using algebraic-geometric code AG(F,63P) [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80 (see above)
  3. linear OA(64¹, 3, F₆₄, 1) (dual of [3, 2, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(64¹, s, F₆₄, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]
linear OA(64⁶⁹, 4097, F₆₄, 35) (dual of [4097, 4028, 36]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 4097Â | 64⁴âˆ’1, defining interval IÂ =Â [0,17], and minimum distance dÂ â‰¥ |{−17,−16,…,17}|+1Â =Â 36 (BCH-bound) [i]

Mode: Constructive and linear.

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