MinT - Information on Result #1415647

Information on Result #1415647

Linear OOA(3²⁰⁹, 2087, F₃, 2, 43) (dual of [(2087, 2), 3965, 44]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(3²⁰⁹, 2087, F₃, 43) (dual of [2087, 1878, 44]-code), using

discarding factors / shortening the dual code based on linear OA(3²⁰⁹, 2228, F₃, 43) (dual of [2228, 2019, 44]-code), using
- 2 times code embedding in larger space [i] based on linear OA(3²⁰⁷, 2226, F₃, 43) (dual of [2226, 2019, 44]-code), using
  - constructionÂ X applied to C([0,21]) âŠ‚ C([0,18]) [i] based on
    1. linear OA(3¹⁹⁷, 2188, F₃, 43) (dual of [2188, 1991, 44]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188Â | 3¹⁴âˆ’1, defining interval IÂ =Â [0,21], and minimum distance dÂ â‰¥ |{−21,−20,…,21}|+1Â =Â 44 (BCH-bound) [i]
    2. linear OA(3¹⁶⁹, 2188, F₃, 37) (dual of [2188, 2019, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188Â | 3¹⁴âˆ’1, defining interval IÂ =Â [0,18], and minimum distance dÂ â‰¥ |{−18,−17,…,18}|+1Â =Â 38 (BCH-bound) [i]
    3. linear OA(3¹⁰, 38, F₃, 5) (dual of [38, 28, 6]-code), using
      - discarding factors / shortening the dual code based on linear OA(3¹⁰, 39, F₃, 5) (dual of [39, 29, 6]-code), using
        generator matrices provided on Edelâ€™s homepage [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(3²⁰⁹, 1043, F₃, 3, 43) (dual of [(1043, 3), 2920, 44]-NRT-code)	[i]		OOA Folding
2	Linear OOA(3²⁰⁹, 1043, F₃, 4, 43) (dual of [(1043, 4), 3963, 44]-NRT-code)	[i]		OOA Folding