MinT - Information on Result #910541

Information on Result #910541

Linear OOA(8¹⁶⁹, 86, F₈, 2, 156) (dual of [(86, 2), 3, 157]-NRT-code), using juxtaposition based on

linear OOA(8²¹, 12, F₈, 2, 20) (dual of [(12, 2), 3, 21]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8²¹, 14, F₈, 2, 20) (dual of [(14, 2), 7, 21]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,7P) [i] based on function field F/F₈ with g(F) = 1 and N(F) ≥ 14, using
    - F₂ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]
linear OOA(8¹⁴⁵, 74, F₈, 2, 135) (dual of [(74, 2), 3, 136]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(8¹⁵, 9, F₈, 2, 15) (dual of [(9, 2), 3, 16]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;3,8) [i]
  2. linear OOA(8¹²⁷, 65, F₈, 2, 119) (dual of [(65, 2), 3, 120]-NRT-code), using
    - standard lengthening with (d₀,â€¦,d₁)Â = (118,119) [i] based on linear OOA(8¹²⁵, 64, F₈, 2, 117) (dual of [(64, 2), 3, 118]-NRT-code), using algebraic-geometric NRT-code AG(2;F,10P) with known gap numbers [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using the Suzuki function field over F₈ [i]

Mode: Constructive and linear.

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