MinT - Information on Result #1028142

Information on Result #1028142

Linear OOA(2¹⁹⁸, 78, F₂, 3, 76) (dual of [(78, 3), 36, 77]-NRT-code), using concatenation of two NRT-codes based on

linear OA(8¹⁴, 26, F₈, 10) (dual of [26, 12, 11]-code), using
- constructionÂ X applied to AG(F,12P) âŠ‚ AG(F,14P) [i] based on
  1. linear OA(8¹³, 23, F₈, 10) (dual of [23, 10, 11]-code), using algebraic-geometric code AG(F,12P) [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(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 (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(2⁶, 3, F₂, 3, 6) (dual of [(3, 3), 3, 7]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(3;3,2) [i]

Mode: Constructive and linear.

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