MinT - Information on Result #669782

Information on Result #669782

Linear OA(64⁸⁷, 262227, F₆₄, 25) (dual of [262227, 262140, 26]-code), using (u,Â u+v)-construction based on

linear OA(64¹⁴, 82, F₆₄, 12) (dual of [82, 68, 13]-code), using
- constructionÂ X applied to AG(F,66P) âŠ‚ AG(F,68P) [i] based on
  1. linear OA(64¹³, 79, F₆₄, 12) (dual of [79, 66, 13]-code), using algebraic-geometric code AG(F,66P) [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(64¹¹, 79, F₆₄, 10) (dual of [79, 68, 11]-code), using algebraic-geometric code AG(F,68P) [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(64⁷³, 262145, F₆₄, 25) (dual of [262145, 262072, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 262145Â | 64⁶âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]

Mode: Constructive and linear.

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