MinT - Information on Result #2767035

Information on Result #2767035

Linear OOA(2²⁴², 62, F₂, 4, 179) (dual of [(62, 4), 6, 180]-NRT-code), using strength reduction based on linear OOA(2²⁴², 62, F₂, 4, 182) (dual of [(62, 4), 6, 183]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(2¹⁸, 6, F₂, 4, 16) (dual of [(6, 4), 6, 17]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(4;F,7P) [i] based on function field F/F₂ with g(F) = 2 and N(F) ≥ 6, using
    - an explicitly constructive algebraic function field [i]
2. linear OOA(2²¹⁸, 56, F₂, 4, 165) (dual of [(56, 4), 6, 166]-NRT-code), using
  - juxtaposition [i] based on
    1. linear OOA(2¹⁸, 6, F₂, 4, 16) (dual of [(6, 4), 6, 17]-NRT-code) (see above)
    2. linear OOA(2¹⁹⁴, 50, F₂, 4, 148) (dual of [(50, 4), 6, 149]-NRT-code), using
      - juxtaposition [i] based on
        linear OOA(2¹⁸, 6, F₂, 4, 16) (dual of [(6, 4), 6, 17]-NRT-code) (see above)
        linear OOA(2¹⁷⁰, 44, F₂, 4, 131) (dual of [(44, 4), 6, 132]-NRT-code), using
        4 step truncation [i] based on linear OOA(2¹⁷⁴, 45, F₂, 4, 135) (dual of [(45, 4), 6, 136]-NRT-code), using
        concatenation of two NRT-codes [i] based on
        linear OA(8⁷, 9, F₈, 7) (dual of [9, 2, 8]-code or 9-arc in PG(6,8)), using
        extended Reedâ€“Solomon code RS_e(2,8) [i]
        Simplex code S(2,8) [i]
        linear OOA(2¹⁷, 5, F₂, 4, 16) (dual of [(5, 4), 3, 17]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(4;F,3P) [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.