MinT - Information on Result #1527219

Information on Result #1527219

Linear OOA(3¹⁹⁰, 9864, F₃, 3, 30) (dual of [(9864, 3), 29402, 31]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁹⁰, 9864, F₃, 2, 30) (dual of [(9864, 2), 19538, 31]-NRT-code), using

OOA 2-folding [i] based on linear OA(3¹⁹⁰, 19728, F₃, 30) (dual of [19728, 19538, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(3¹⁹⁰, 19729, F₃, 30) (dual of [19729, 19539, 31]-code), using
  - constructionÂ X applied to C([0,15]) âŠ‚ C([0,12]) [i] based on
    1. linear OA(3¹⁸¹, 19684, F₃, 31) (dual of [19684, 19503, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684Â | 3¹⁸âˆ’1, defining interval IÂ =Â [0,15], and minimum distance dÂ â‰¥ |{−15,−14,…,15}|+1Â =Â 32 (BCH-bound) [i]
    2. linear OA(3¹⁴⁵, 19684, F₃, 25) (dual of [19684, 19539, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684Â | 3¹⁸âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
    3. linear OA(3⁹, 45, F₃, 4) (dual of [45, 36, 5]-code), using
      - discarding factors / shortening the dual code based on linear OA(3⁹, 80, F₃, 4) (dual of [80, 71, 5]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 80Â = 3⁴âˆ’1, defining interval IÂ =Â [0,2], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [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(3¹⁹⁰, 4932, F₃, 5, 30) (dual of [(4932, 5), 24470, 31]-NRT-code)	[i]		OOA Folding