MinT - Information on Result #1418610

Information on Result #1418610

Linear OOA(3²³⁹, 14768, F₃, 2, 36) (dual of [(14768, 2), 29297, 37]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(3²³⁹, 14768, F₃, 36) (dual of [14768, 14529, 37]-code), using

discarding factors / shortening the dual code based on linear OA(3²³⁹, 19760, F₃, 36) (dual of [19760, 19521, 37]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3²³⁸, 19759, F₃, 36) (dual of [19759, 19521, 37]-code), using
  - constructionÂ X applied to C([0,18]) âŠ‚ C([0,13]) [i] based on
    1. linear OA(3²¹⁷, 19684, F₃, 37) (dual of [19684, 19467, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684Â | 3¹⁸âˆ’1, defining interval IÂ =Â [0,18], and minimum distance dÂ â‰¥ |{−18,−17,…,18}|+1Â =Â 38 (BCH-bound) [i]
    2. linear OA(3¹⁶³, 19684, F₃, 27) (dual of [19684, 19521, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684Â | 3¹⁸âˆ’1, defining interval IÂ =Â [0,13], and minimum distance dÂ â‰¥ |{−13,−12,…,13}|+1Â =Â 28 (BCH-bound) [i]
    3. linear OA(3²¹, 75, F₃, 8) (dual of [75, 54, 9]-code), using
      - discarding factors / shortening the dual code based on linear OA(3²¹, 80, F₃, 8) (dual of [80, 59, 9]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 80Â = 3⁴âˆ’1, defining interval IÂ =Â [0,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [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(3²³⁹, 7384, F₃, 3, 36) (dual of [(7384, 3), 21913, 37]-NRT-code)	[i]		OOA Folding
2	Linear OOA(3²³⁹, 7384, F₃, 4, 36) (dual of [(7384, 4), 29297, 37]-NRT-code)	[i]		OOA Folding