MinT - Information on Result #809196

Information on Result #809196

Linear OOA(2⁹³, 51, F₂, 2, 47) (dual of [(51, 2), 9, 48]-NRT-code), using OOA 2-folding based on linear OA(2⁹³, 102, F₂, 47) (dual of [102, 9, 48]-code), using

(u,Â u+v)-construction [i] based on
1. linear OA(2⁴³, 51, F₂, 23) (dual of [51, 8, 24]-code), using
  - concatenation of two 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 OA(2¹, 3, F₂, 1) (dual of [3, 2, 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]
2. linear OA(2⁵⁰, 51, F₂, 47) (dual of [51, 1, 48]-code), using
  - strength reduction [i] based on linear OA(2⁵⁰, 51, F₂, 50) (dual of [51, 1, 51]-code or 51-arc in PG(49,2)), using
    - dual of repetition code with length 51 [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.