MinT - Information on Result #911226

Information on Result #911226

Linear OOA(2¹³⁸, 81, F₂, 2, 63) (dual of [(81, 2), 24, 64]-NRT-code), using concatenation of two NRT-codes based on

linear OA(8¹⁹, 27, F₈, 15) (dual of [27, 8, 16]-code), using
- constructionÂ X applied to AG(F,4P) âŠ‚ AG(F,5P) [i] based on
  1. linear OA(8¹⁸, 24, F₈, 15) (dual of [24, 6, 16]-code), using algebraic-geometric code AG(F,4P) with degPÂ =Â 2 [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(8¹⁶, 24, F₈, 13) (dual of [24, 8, 14]-code), using algebraic-geometric code AG(F,5P) with degPÂ =Â 2 [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 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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