MinT - Information on Result #2194227

Information on Result #2194227

Linear OA(3¹⁶⁹, 176, F₃, 108) (dual of [176, 7, 109]-code), using strength reduction based on linear OA(3¹⁶⁹, 176, F₃, 109) (dual of [176, 7, 110]-code), using

juxtaposition [i] based on
1. linear OA(3¹, 8, F₃, 1) (dual of [8, 7, 2]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹, s, F₃, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
    - parity-check code [i]
2. linear OA(3¹⁶¹, 168, F₃, 107) (dual of [168, 7, 108]-code), using
  - (u,Â uâˆ’v,Â u+v+w)-construction [i] based on
    1. linear OA(3⁵⁰, 56, F₃, 35) (dual of [56, 6, 36]-code), using
      - dual code (with bound on d by constructionÂ Y1) [i] based on
        linear OA(3⁶, 56, F₃, 3) (dual of [56, 50, 4]-code or 56-cap in PG(5,3)), using
        the Hill cap [i]
        nonexistence of linear OA(3⁵, 21, F₃, 3) (dual of [21, 16, 4]-code or 21-cap in PG(4,3)), because
        20 is the largest size of a cap in PG(4,Â 3) [i]
    2. linear OA(3⁵⁵, 56, F₃, 53) (dual of [56, 1, 54]-code), using
      - strength reduction [i] based on linear OA(3⁵⁵, 56, F₃, 55) (dual of [56, 1, 56]-code or 56-arc in PG(54,3)), using
        dual of repetition code with length 56 [i]
    3. linear OA(3⁵⁶, 56, F₃, 56) (dual of [56, 0, 57]-code or 56-arc in PG(55,3)), using
      - complete OA / dual of code with only one code word [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

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3¹⁶⁹, 88, F₃, 2, 108) (dual of [(88, 2), 7, 109]-NRT-code)	[i]		OOA Folding