MinT - Information on Result #1614958

Information on Result #1614958

Linear OOA(128⁶⁶, 5817, F₁₂₈, 4, 31) (dual of [(5817, 4), 23202, 32]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(128⁶⁶, 5817, F₁₂₈, 2, 31) (dual of [(5817, 2), 11568, 32]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(128⁶⁶, 8201, F₁₂₈, 2, 31) (dual of [(8201, 2), 16336, 32]-NRT-code), using
- OOA 2-folding [i] based on linear OA(128⁶⁶, 16402, F₁₂₈, 31) (dual of [16402, 16336, 32]-code), using
  - constructionÂ X applied to C([0,15]) âŠ‚ C([0,12]) [i] based on
    1. linear OA(128⁶¹, 16385, F₁₂₈, 31) (dual of [16385, 16324, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 128⁴âˆ’1, defining interval IÂ =Â [0,15], and minimum distance dÂ â‰¥ |{−15,−14,…,15}|+1Â =Â 32 (BCH-bound) [i]
    2. linear OA(128⁴⁹, 16385, F₁₂₈, 25) (dual of [16385, 16336, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 128⁴âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
    3. linear OA(128⁵, 17, F₁₂₈, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,128)), using
      - discarding factors / shortening the dual code based on linear OA(128⁵, 128, F₁₂₈, 5) (dual of [128, 123, 6]-code or 128-arc in PG(4,128)), using
        Reedâ€“Solomon code RS(123,128) [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(128⁶⁶, 1454, F₁₂₈, 36, 31) (dual of [(1454, 36), 52278, 32]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row