MinT - Information on Result #2418341

Information on Result #2418341

Linear OOA(2¹⁰¹, 53, F₂, 2, 63) (dual of [(53, 2), 5, 64]-NRT-code), using strength reduction based on linear OOA(2¹⁰¹, 53, F₂, 2, 64) (dual of [(53, 2), 5, 65]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(2⁵, 5, F₂, 2, 4) (dual of [(5, 2), 5, 5]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,5P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, using
    - an explicitly constructive algebraic function field [i]
2. linear OOA(2⁹¹, 48, F₂, 2, 59) (dual of [(48, 2), 5, 60]-NRT-code), using
  - 2¹ times duplication [i] based on linear OOA(2⁹⁰, 48, F₂, 2, 59) (dual of [(48, 2), 6, 60]-NRT-code), using
    - concatenation of two NRT-codes [i] based on
      1. linear OA(4¹³, 16, F₄, 11) (dual of [16, 3, 12]-code), using
        discarding factors / shortening the dual code based on linear OA(4¹³, 17, F₄, 11) (dual of [17, 4, 12]-code), using
        projective code from ovoid in PG(3,Â 4) [i]
      2. linear OOA(2⁴, 3, F₂, 2, 4) (dual of [(3, 2), 2, 5]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;2,2) [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.