MinT - Information on Result #1615086

Information on Result #1615086

Linear OOA(128⁷², 7817, F₁₂₈, 4, 33) (dual of [(7817, 4), 31196, 34]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(128⁷², 7817, F₁₂₈, 2, 33) (dual of [(7817, 2), 15562, 34]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(128⁷², 8204, F₁₂₈, 2, 33) (dual of [(8204, 2), 16336, 34]-NRT-code), using
- OOA 2-folding [i] based on linear OA(128⁷², 16408, F₁₂₈, 33) (dual of [16408, 16336, 34]-code), using
  - constructionÂ X applied to C([0,16]) âŠ‚ C([0,12]) [i] based on
    1. linear OA(128⁶⁵, 16385, F₁₂₈, 33) (dual of [16385, 16320, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 128⁴âˆ’1, defining interval IÂ =Â [0,16], and minimum distance dÂ â‰¥ |{−16,−15,…,16}|+1Â =Â 34 (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(128⁷, 23, F₁₂₈, 7) (dual of [23, 16, 8]-code or 23-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(128⁷², 1954, F₁₂₈, 36, 33) (dual of [(1954, 36), 70272, 34]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row