MinT - Information on Result #663902

Information on Result #663902

Linear OA(8¹¹¹, 2097179, F₈, 17) (dual of [2097179, 2097068, 18]-code), using (u,Â u+v)-construction based on

linear OA(8¹², 26, F₈, 8) (dual of [26, 14, 9]-code), using
- constructionÂ X applied to AG(F,14P) âŠ‚ AG(F,16P) [i] based on
  1. linear OA(8¹¹, 23, F₈, 8) (dual of [23, 12, 9]-code), using algebraic-geometric code AG(F,14P) [i] based on function field F/F₈ with g(F) = 3 and N(F) ≥ 24, using
    - the Klein quartic over F₈ [i]
  2. linear OA(8⁹, 23, F₈, 6) (dual of [23, 14, 7]-code), using algebraic-geometric code AG(F,16P) [i] based on function field F/F₈ with g(F) = 3 and N(F) ≥ 24 (see above)
  3. linear OA(8¹, 3, F₈, 1) (dual of [3, 2, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(8¹, s, F₈, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]
linear OA(8⁹⁹, 2097153, F₈, 17) (dual of [2097153, 2097054, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 2097153Â | 8¹⁴âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]

Mode: Constructive and linear.

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