MinT - Information on Result #911328

Information on Result #911328

Linear OOA(2²⁴³, 147, F₂, 2, 87) (dual of [(147, 2), 51, 88]-NRT-code), using concatenation of two NRT-codes based on

linear OA(8³², 49, F₈, 21) (dual of [49, 17, 22]-code), using
- constructionÂ X applied to AG(F,22P) âŠ‚ AG(F,25P) [i] based on
  1. linear OA(8³⁰, 44, F₈, 21) (dual of [44, 14, 22]-code), using algebraic-geometric code AG(F,22P) [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
    - an explicitly constructive algebraic function field [i]
  2. linear OA(8²⁷, 44, F₈, 18) (dual of [44, 17, 19]-code), using algebraic-geometric code AG(F,25P) [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45 (see above)
  3. linear OA(8², 5, F₈, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,8)), using
    - discarding factors / shortening the dual code based on linear OA(8², 8, F₈, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,8)), using
      - Reedâ€“Solomon code RS(6,8) [i]
linear OOA(2³, 3, F₂, 2, 3) (dual of [(3, 2), 3, 4]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(2;3,2) [i]

Mode: Constructive and linear.

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