MinT - Information on Result #1027970

Information on Result #1027970

Linear OOA(2¹³⁸, 52, F₂, 3, 67) (dual of [(52, 3), 18, 68]-NRT-code), using concatenation of two NRT-codes based on

linear OA(8²⁰, 26, F₈, 16) (dual of [26, 6, 17]-code), using
- constructionÂ X applied to AG(F,6P) âŠ‚ AG(F,8P) [i] based on
  1. linear OA(8¹⁹, 23, F₈, 16) (dual of [23, 4, 17]-code), using algebraic-geometric code AG(F,6P) [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(8¹⁷, 23, F₈, 14) (dual of [23, 6, 15]-code), using algebraic-geometric code AG(F,8P) [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, 2, F₂, 3, 3) (dual of [(2, 3), 3, 4]-NRT-code), using
- Reedâ€“Solomon NRT-code RS(3;3,2) [i]

Mode: Constructive and linear.

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