MinT - Information on Result #1523106

Information on Result #1523106

Linear OOA(3¹²⁸, 8242, F₃, 3, 21) (dual of [(8242, 3), 24598, 22]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹²⁸, 8242, F₃, 2, 21) (dual of [(8242, 2), 16356, 22]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹²⁸, 9851, F₃, 2, 21) (dual of [(9851, 2), 19574, 22]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3¹²⁸, 19702, F₃, 21) (dual of [19702, 19574, 22]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹²⁸, 19703, F₃, 21) (dual of [19703, 19575, 22]-code), using
    - constructionÂ X applied to C([0,10]) âŠ‚ C([0,9]) [i] based on
      1. linear OA(3¹²⁷, 19684, F₃, 21) (dual of [19684, 19557, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684Â | 3¹⁸âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (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(3¹, 19, F₃, 1) (dual of [19, 18, 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(3¹²⁸, 4121, F₃, 5, 21) (dual of [(4121, 5), 20477, 22]-NRT-code)	[i]		OOA Folding