MinT - Information on Result #1058911

Information on Result #1058911

Linear OOA(2²⁰⁵, 53, F₂, 4, 122) (dual of [(53, 4), 7, 123]-NRT-code), using OOA 2-folding based on linear OOA(2²⁰⁵, 106, F₂, 2, 122) (dual of [(106, 2), 7, 123]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(2³⁹, 23, F₂, 2, 23) (dual of [(23, 2), 7, 24]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(2³⁹, 24, F₂, 2, 23) (dual of [(24, 2), 9, 24]-NRT-code), using
    - concatenation of two NRT-codes [i] based on
      1. linear OA(8⁵, 8, F₈, 5) (dual of [8, 3, 6]-code or 8-arc in PG(4,8)), using
        Reedâ€“Solomon code RS(3,8) [i]
      2. linear OOA(2³, 3, F₂, 2, 3) (dual of [(3, 2), 3, 4]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;3,2) [i]
2. linear OOA(2¹⁵⁹, 83, F₂, 2, 98) (dual of [(83, 2), 7, 99]-NRT-code), using
  - 1 step truncation [i] based on linear OOA(2¹⁶⁰, 84, F₂, 2, 99) (dual of [(84, 2), 8, 100]-NRT-code), using
    - concatenation of two NRT-codes [i] based on
      1. linear OA(4²⁴, 28, F₄, 19) (dual of [28, 4, 20]-code), using
        an explicit generator matrix [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.