MinT - Information on Result #1601583

Information on Result #1601583

Linear OOA(3⁶⁴, 33258, F₃, 4, 9) (dual of [(33258, 4), 132968, 10]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(3⁶⁴, 33258, F₃, 9) (dual of [33258, 33194, 10]-code), using

discarding factors / shortening the dual code based on linear OA(3⁶⁴, 59074, F₃, 9) (dual of [59074, 59010, 10]-code), using
- 2 times code embedding in larger space [i] based on linear OA(3⁶², 59072, F₃, 9) (dual of [59072, 59010, 10]-code), using
  - constructionÂ X4 applied to C([0,4]) âŠ‚ C([0,3]) [i] based on
    1. linear OA(3⁶¹, 59050, F₃, 9) (dual of [59050, 58989, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050Â | 3²⁰âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (BCH-bound) [i]
    2. linear OA(3⁴¹, 59050, F₃, 7) (dual of [59050, 59009, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050Â | 3²⁰âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (BCH-bound) [i]
    3. linear OA(3²¹, 22, F₃, 21) (dual of [22, 1, 22]-code or 22-arc in PG(20,3)), using
      - dual of repetition code with length 22 [i]
    4. linear OA(3¹, 22, F₃, 1) (dual of [22, 21, 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]

Mode: 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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3⁶⁴, 33257, F₃, 5, 9) (dual of [(33257, 5), 166221, 10]-NRT-code)	[i]		OOA Stacking with Additional Row
2	Linear OOA(3⁶⁴, 33257, F₃, 12, 9) (dual of [(33257, 12), 399020, 10]-NRT-code)	[i]		OOA Stacking with Additional Row