MinT - Information on Result #2766782

Information on Result #2766782

Linear OOA(2²³⁸, 61, F₂, 4, 176) (dual of [(61, 4), 6, 177]-NRT-code), using strength reduction based on linear OOA(2²³⁸, 61, F₂, 4, 178) (dual of [(61, 4), 6, 179]-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(2²¹⁴, 55, F₂, 4, 161) (dual of [(55, 4), 6, 162]-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(2¹⁹⁰, 49, F₂, 4, 144) (dual of [(49, 4), 6, 145]-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(2¹⁶⁶, 43, F₂, 4, 127) (dual of [(43, 4), 6, 128]-NRT-code), using
        8 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.