MinT - Information on Result #1649673

Information on Result #1649673

Linear OOA(3²¹⁸, 135957, F₃, 5, 27) (dual of [(135957, 5), 679567, 28]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²¹⁸, 135957, F₃, 3, 27) (dual of [(135957, 3), 407653, 28]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3²¹⁸, 177155, F₃, 3, 27) (dual of [(177155, 3), 531247, 28]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3²¹⁸, 531465, F₃, 27) (dual of [531465, 531247, 28]-code), using
  - discarding factors / shortening the dual code based on linear OA(3²¹⁸, 531467, F₃, 27) (dual of [531467, 531249, 28]-code), using
    - constructionÂ X applied to C([0,13]) âŠ‚ C([0,12]) [i] based on
      1. linear OA(3²¹⁷, 531442, F₃, 27) (dual of [531442, 531225, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442Â | 3²⁴âˆ’1, defining interval IÂ =Â [0,13], and minimum distance dÂ â‰¥ |{−13,−12,…,13}|+1Â =Â 28 (BCH-bound) [i]
      2. linear OA(3¹⁹³, 531442, F₃, 25) (dual of [531442, 531249, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442Â | 3²⁴âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
      3. linear OA(3¹, 25, F₃, 1) (dual of [25, 24, 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(3²¹⁸, 45318, F₃, 35, 27) (dual of [(45318, 35), 1585912, 28]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row