MinT - Information on Result #911347

Information on Result #911347

Linear OOA(2²⁴³, 141, F₂, 2, 99) (dual of [(141, 2), 39, 100]-NRT-code), using concatenation of two NRT-codes based on

linear OA(8³⁴, 47, F₈, 24) (dual of [47, 13, 25]-code), using
- constructionÂ X applied to AG(F,19P) âŠ‚ AG(F,21P) [i] based on
  1. linear OA(8³³, 44, F₈, 24) (dual of [44, 11, 25]-code), using algebraic-geometric code AG(F,19P) [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(8³¹, 44, F₈, 22) (dual of [44, 13, 23]-code), using algebraic-geometric code AG(F,21P) [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45 (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 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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