MinT - Information on Result #2418554

Information on Result #2418554

Linear OOA(2¹⁰⁶, 57, F₂, 2, 58) (dual of [(57, 2), 8, 59]-NRT-code), using strength reduction based on linear OOA(2¹⁰⁶, 57, F₂, 2, 61) (dual of [(57, 2), 8, 62]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(2⁸, 8, F₂, 2, 5) (dual of [(8, 2), 8, 6]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(2⁸, 10, F₂, 2, 5) (dual of [(10, 2), 12, 6]-NRT-code), using
    - extracting embedded OOA [i] based on digital (3, 8, 10)-net over F₂, using
      - linear code embedding found in a computer search [i]
2. linear OOA(2⁹⁰, 49, F₂, 2, 55) (dual of [(49, 2), 8, 56]-NRT-code), using
  - 4 step truncation [i] based on linear OOA(2⁹⁴, 51, F₂, 2, 59) (dual of [(51, 2), 8, 60]-NRT-code), using
    - concatenation of two NRT-codes [i] based on
      1. 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.