MinT - Information on Result #1464909

Information on Result #1464909

Linear OOA(128⁶⁸, 14562, F₁₂₈, 2, 29) (dual of [(14562, 2), 29056, 30]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(128⁶⁸, 14562, F₁₂₈, 29) (dual of [14562, 14494, 30]-code), using

discarding factors / shortening the dual code based on linear OA(128⁶⁸, 16420, F₁₂₈, 29) (dual of [16420, 16352, 30]-code), using
- constructionÂ X applied to C([0,14]) âŠ‚ C([0,8]) [i] based on
  1. linear OA(128⁵⁷, 16385, F₁₂₈, 29) (dual of [16385, 16328, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 128⁴âˆ’1, defining interval IÂ =Â [0,14], and minimum distance dÂ â‰¥ |{−14,−13,…,14}|+1Â =Â 30 (BCH-bound) [i]
  2. linear OA(128³³, 16385, F₁₂₈, 17) (dual of [16385, 16352, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 128⁴âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]
  3. linear OA(128¹¹, 35, F₁₂₈, 11) (dual of [35, 24, 12]-code or 35-arc in PG(10,128)), using
    - discarding factors / shortening the dual code based on linear OA(128¹¹, 128, F₁₂₈, 11) (dual of [128, 117, 12]-code or 128-arc in PG(10,128)), using
      - Reedâ€“Solomon code RS(117,128) [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(128⁶⁸, 7281, F₁₂₈, 3, 29) (dual of [(7281, 3), 21775, 30]-NRT-code)	[i]		OOA Folding
2	Linear OOA(128⁶⁸, 7281, F₁₂₈, 4, 29) (dual of [(7281, 4), 29056, 30]-NRT-code)	[i]		OOA Folding