MinT - Information on Result #1608775

Information on Result #1608775

Linear OOA(3²⁰², 177166, F₃, 4, 24) (dual of [(177166, 4), 708462, 25]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²⁰², 177166, F₃, 3, 24) (dual of [(177166, 3), 531296, 25]-NRT-code), using

OOA 3-folding [i] based on linear OA(3²⁰², 531498, F₃, 24) (dual of [531498, 531296, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(3²⁰², 531499, F₃, 24) (dual of [531499, 531297, 25]-code), using
  - constructionÂ X applied to C([0,12]) âŠ‚ C([0,9]) [i] based on
    1. 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]
    2. linear OA(3¹⁴⁵, 531442, F₃, 19) (dual of [531442, 531297, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442Â | 3²⁴âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]
    3. linear OA(3⁹, 57, F₃, 4) (dual of [57, 48, 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(3²⁰³, 177166, F₃, 4, 24) (dual of [(177166, 4), 708461, 25]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(3²⁰², 59055, F₃, 28, 24) (dual of [(59055, 28), 1653338, 25]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row