MinT - Information on Result #2266849

Information on Result #2266849

Linear OA(3⁶³, 69, F₃, 41) (dual of [69, 6, 42]-code), using 1 times code embedding in larger space based on linear OA(3⁶², 68, F₃, 41) (dual of [68, 6, 42]-code), using

juxtaposition [i] based on
1. linear OA(3⁶, 12, F₃, 5) (dual of [12, 6, 6]-code), using
  - extended Golay code G_e(3) [i]
2. 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]

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(3⁶³, 23, F₃, 3, 41) (dual of [(23, 3), 6, 42]-NRT-code)	[i]		OOA Folding