MinT - Information on Result #1646610

Information on Result #1646610

Linear OOA(3¹⁸⁰, 1370134, F₃, 5, 19) (dual of [(1370134, 5), 6850490, 20]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁸⁰, 1370134, F₃, 3, 19) (dual of [(1370134, 3), 4110222, 20]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁸⁰, 1594345, F₃, 3, 19) (dual of [(1594345, 3), 4782855, 20]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3¹⁸⁰, 4783035, F₃, 19) (dual of [4783035, 4782855, 20]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁸⁰, 4783037, F₃, 19) (dual of [4783037, 4782857, 20]-code), using
    - constructionÂ X applied to C([0,9]) âŠ‚ C([0,6]) [i] based on
      1. linear OA(3¹⁶⁹, 4782970, F₃, 19) (dual of [4782970, 4782801, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 4782970Â | 3²⁸âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]
      2. linear OA(3¹¹³, 4782970, F₃, 13) (dual of [4782970, 4782857, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 4782970Â | 3²⁸âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]
      3. linear OA(3¹¹, 67, F₃, 5) (dual of [67, 56, 6]-code), using
        discarding factors / shortening the dual code based on linear OA(3¹¹, 85, F₃, 5) (dual of [85, 74, 6]-code), using
        codes constructed by inverting constructionÂ Y₁ [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(3¹⁸⁰, 685066, F₃, 25, 19) (dual of [(685066, 25), 17126470, 20]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row