MinT - Information on Result #1605586

Information on Result #1605586

Linear OOA(3¹⁵⁸, 11480, F₃, 4, 24) (dual of [(11480, 4), 45762, 25]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(3¹⁵⁸, 11480, F₃, 24) (dual of [11480, 11322, 25]-code), using

discarding factors / shortening the dual code based on linear OA(3¹⁵⁸, 19733, F₃, 24) (dual of [19733, 19575, 25]-code), using
- 4 times code embedding in larger space [i] based on linear OA(3¹⁵⁴, 19729, F₃, 24) (dual of [19729, 19575, 25]-code), using
  - constructionÂ X applied to C([0,12]) âŠ‚ C([0,9]) [i] based on
    1. 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]
    2. linear OA(3¹⁰⁹, 19684, F₃, 19) (dual of [19684, 19575, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684Â | 3¹⁸âˆ’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, 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(3¹⁵⁸, 3826, F₃, 28, 24) (dual of [(3826, 28), 106970, 25]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row