MinT - Information on Result #2483104

Information on Result #2483104

Linear OOA(2²⁴⁹, 181, F₂, 2, 86) (dual of [(181, 2), 113, 87]-NRT-code), using 2¹ times duplication based on linear OOA(2²⁴⁸, 181, F₂, 2, 86) (dual of [(181, 2), 114, 87]-NRT-code), using

1 times NRT-code embedding in larger space [i] based on linear OOA(2²⁴⁶, 180, F₂, 2, 86) (dual of [(180, 2), 114, 87]-NRT-code), using
- strength reduction [i] based on linear OOA(2²⁴⁶, 180, F₂, 2, 87) (dual of [(180, 2), 114, 88]-NRT-code), using
  - concatenation of two NRT-codes [i] based on
    1. linear OOA(8⁵², 45, F₈, 2, 43) (dual of [(45, 2), 38, 44]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(2;F,46P) [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
        an explicitly constructive algebraic function field [i]
    2. linear OA(2¹, 4, F₂, 1) (dual of [4, 3, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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.