MinT - Information on Result #806622

Information on Result #806622

Linear OOA(2⁶⁶, 49, F₂, 2, 22) (dual of [(49, 2), 32, 23]-NRT-code), using OOA 2-folding based on linear OA(2⁶⁶, 98, F₂, 22) (dual of [98, 32, 23]-code), using

1 times truncation [i] based on linear OA(2⁶⁷, 99, F₂, 23) (dual of [99, 32, 24]-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OA(2²⁴, 48, F₂, 11) (dual of [48, 24, 12]-code), using
    - extended quadratic residue code Q_e(48,2) [i]
  2. 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]

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.