MinT - Information on Result #640846

Information on Result #640846

Linear OA(2¹⁰⁸, 116, F₂, 52) (dual of [116, 8, 53]-code), using juxtaposition based on

linear OA(2³⁹, 47, F₂, 20) (dual of [47, 8, 21]-code), using
- 1 times truncation [i] based on linear OA(2⁴⁰, 48, F₂, 21) (dual of [48, 8, 22]-code), using
  - concatenation of two codes [i] based on
    1. linear OA(4¹², 16, F₄, 10) (dual of [16, 4, 11]-code), using
      - 1 times truncation [i] based on 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]
linear OA(2⁶¹, 69, F₂, 31) (dual of [69, 8, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(2⁶¹, 70, F₂, 31) (dual of [70, 9, 32]-code), using
  - concatenation of two codes [i] based on
    1. linear OA(8⁷, 10, F₈, 7) (dual of [10, 3, 8]-code or 10-arc in PG(6,8)), using
      - Denniston code D(1,8) [i]
    2. linear OA(2⁴, 7, F₂, 3) (dual of [7, 3, 4]-code or 7-cap in PG(3,2)), using
      - Simplex code S(3,2) [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.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

None.