MinT - Information on Result #1464915

Information on Result #1464915

Linear OOA(128⁶⁸, 1683051, F₁₂₈, 2, 21) (dual of [(1683051, 2), 3366034, 22]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(128⁶⁸, 1683051, F₁₂₈, 21) (dual of [1683051, 1682983, 22]-code), using

discarding factors / shortening the dual code based on linear OA(128⁶⁸, 2097184, F₁₂₈, 21) (dual of [2097184, 2097116, 22]-code), using
- constructionÂ X applied to C([0,10]) âŠ‚ C([0,6]) [i] based on
  1. linear OA(128⁶¹, 2097153, F₁₂₈, 21) (dual of [2097153, 2097092, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153Â | 128⁶âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]
  2. linear OA(128³⁷, 2097153, F₁₂₈, 13) (dual of [2097153, 2097116, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153Â | 128⁶âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]
  3. linear OA(128⁷, 31, F₁₂₈, 7) (dual of [31, 24, 8]-code or 31-arc in PG(6,128)), using
    - discarding factors / shortening the dual code based on linear OA(128⁷, 128, F₁₂₈, 7) (dual of [128, 121, 8]-code or 128-arc in PG(6,128)), using
      - Reedâ€“Solomon code RS(121,128) [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, 841525, F₁₂₈, 3, 21) (dual of [(841525, 3), 2524507, 22]-NRT-code)	[i]		OOA Folding
2	Linear OOA(128⁶⁸, 841525, F₁₂₈, 4, 21) (dual of [(841525, 4), 3366032, 22]-NRT-code)	[i]		OOA Folding