MinT - Information on Result #2193802

Information on Result #2193802

Linear OA(3¹⁶¹, 168, F₃, 105) (dual of [168, 7, 106]-code), using strength reduction based on 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
    1. linear OA(3⁶, 56, F₃, 3) (dual of [56, 50, 4]-code or 56-cap in PG(5,3)), using
      - the Hill cap [i]
    2. 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		Method
1	Linear OA(3¹⁶⁰, 167, F₃, 104) (dual of [167, 7, 105]-code)	[i]	Truncation
2	Linear OA(3¹⁵⁹, 166, F₃, 103) (dual of [166, 7, 104]-code)	[i]
3	Linear OA(3¹⁵⁸, 165, F₃, 102) (dual of [165, 7, 103]-code)	[i]
4	Linear OA(3¹⁵⁷, 164, F₃, 101) (dual of [164, 7, 102]-code)	[i]
5	Linear OA(3¹⁵⁶, 163, F₃, 100) (dual of [163, 7, 101]-code)	[i]
6	Linear OOA(3¹⁶¹, 56, F₃, 3, 105) (dual of [(56, 3), 7, 106]-NRT-code)	[i]	OOA Folding