MinT - Information on Result #1129648

Information on Result #1129648

Linear OOA(2²⁵⁷, 53, F₂, 5, 196) (dual of [(53, 5), 8, 197]-NRT-code), using juxtaposition based on

linear OOA(2³², 8, F₂, 5, 28) (dual of [(8, 5), 8, 29]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(5;F,11P) [i] based on function field F/F₂ with g(F) = 4 and N(F) ≥ 8, using
  - an explicitly constructive algebraic function field [i]
linear OOA(2²¹⁷, 45, F₂, 5, 167) (dual of [(45, 5), 8, 168]-NRT-code), using
- concatenation of two NRT-codes [i] based on
  1. linear OA(16¹³, 15, F₁₆, 13) (dual of [15, 2, 14]-code or 15-arc in PG(12,16)), using
    - discarding factors / shortening the dual code based on linear OA(16¹³, 16, F₁₆, 13) (dual of [16, 3, 14]-code or 16-arc in PG(12,16)), using
      - Reedâ€“Solomon code RS(3,16) [i]
  2. linear OOA(2¹¹, 3, F₂, 5, 11) (dual of [(3, 5), 4, 12]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(5;4,2) [i]

Mode: Constructive and linear.

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