MinT - Information on Result #911373

Information on Result #911373

Linear OOA(2²⁵⁵, 141, F₂, 2, 115) (dual of [(141, 2), 27, 116]-NRT-code), using concatenation of two NRT-codes based on

linear OA(8³⁸, 47, F₈, 28) (dual of [47, 9, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(8³⁸, 48, F₈, 28) (dual of [48, 10, 29]-code), using
  - constructionÂ X applied to AG(F,8P) âŠ‚ AG(F,9P) [i] based on
    1. linear OA(8³⁷, 45, F₈, 28) (dual of [45, 8, 29]-code), using algebraic-geometric code AG(F,8P) with degPÂ =Â 2 [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(8³⁵, 45, F₈, 26) (dual of [45, 10, 27]-code), using algebraic-geometric code AG(F,9P) with degPÂ =Â 2 [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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