MinT - Information on Result #2228699

Information on Result #2228699

Linear OA(3⁸², 117, F₃, 34) (dual of [117, 35, 35]-code), using 1 times truncation based on linear OA(3⁸³, 118, F₃, 35) (dual of [118, 35, 36]-code), using

(u,Â u+v)-construction [i] based on
1. linear OA(3³⁰, 59, F₃, 17) (dual of [59, 29, 18]-code), using
  - discarding factors / shortening the dual code based on linear OA(3³⁰, 60, F₃, 17) (dual of [60, 30, 18]-code), using
    - extended quadratic residue code Q_e(60,3) [i]
2. linear OA(3⁵³, 59, F₃, 35) (dual of [59, 6, 36]-code), using
  - 3 times code embedding in larger space [i] based on 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(3⁸², 58, F₃, 2, 34) (dual of [(58, 2), 34, 35]-NRT-code)	[i]		OOA Folding
2	Linear OOA(3⁸², 39, F₃, 3, 34) (dual of [(39, 3), 35, 35]-NRT-code)	[i]		OOA Folding