MinT - Information on Result #671892

Information on Result #671892

Linear OA(2²⁰⁵, 218, F₂, 94) (dual of [218, 13, 95]-code), using juxtaposition based on

linear OA(2¹⁴, 27, F₂, 6) (dual of [27, 13, 7]-code), using
- 1 times truncation [i] based on linear OA(2¹⁵, 28, F₂, 7) (dual of [28, 13, 8]-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OA(2³, 4, F₂, 3) (dual of [4, 1, 4]-code or 4-arc in PG(2,2) or 4-cap in PG(2,2)), using
      - dual of repetition code with length 4 [i]
      - caps in base bÂ =Â 2 [i]
    2. linear OA(2¹², 24, F₂, 7) (dual of [24, 12, 8]-code), using
      - extended Golay code G_e(2) [i]
linear OA(2¹⁷⁸, 191, F₂, 87) (dual of [191, 13, 88]-code), using
- discarding factors / shortening the dual code based on linear OA(2¹⁷⁸, 192, F₂, 87) (dual of [192, 14, 88]-code), using
  - concatenation of two codes [i] based on
    1. linear OA(4⁵⁷, 64, F₄, 43) (dual of [64, 7, 44]-code), using
      - an extension C_e(42) of the primitive narrow-sense BCH-code C(I) with length 63Â = 4³âˆ’1, defining interval IÂ =Â [1,42], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 43 [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.

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

Other Results with Identical Parameters

None.

Depending Results

None.