MinT - Information on Result #2619948

Information on Result #2619948

Linear OOA(2²⁵⁷, 88, F₂, 3, 175) (dual of [(88, 3), 7, 176]-NRT-code), using strength reduction based on linear OOA(2²⁵⁷, 88, F₂, 3, 178) (dual of [(88, 3), 7, 179]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(2¹⁷, 8, F₂, 3, 13) (dual of [(8, 3), 7, 14]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,10P) [i] based on function field F/F₂ with g(F) = 4 and N(F) ≥ 8, using
    - an explicitly constructive algebraic function field [i]
2. linear OOA(2²³³, 80, F₂, 3, 164) (dual of [(80, 3), 7, 165]-NRT-code), using
  - 2¹ times duplication [i] based on linear OOA(2²³², 80, F₂, 3, 164) (dual of [(80, 3), 8, 165]-NRT-code), using
    - concatenation of two NRT-codes [i] based on
      1. linear OA(16¹⁴, 16, F₁₆, 14) (dual of [16, 2, 15]-code or 16-arc in PG(13,16)), using
        Reedâ€“Solomon code RS(2,16) [i]
      2. linear OOA(2¹¹, 5, F₂, 3, 10) (dual of [(5, 3), 4, 11]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(3;F,4P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, using
        an explicitly constructive algebraic function field [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

None.