MinT - Information on Result #1615042

Information on Result #1615042

Linear OOA(128⁷⁰, 5652, F₁₂₈, 4, 33) (dual of [(5652, 4), 22538, 34]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(128⁷⁰, 5652, F₁₂₈, 2, 33) (dual of [(5652, 2), 11234, 34]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(128⁷⁰, 8201, F₁₂₈, 2, 33) (dual of [(8201, 2), 16332, 34]-NRT-code), using
- OOA 2-folding [i] based on linear OA(128⁷⁰, 16402, F₁₂₈, 33) (dual of [16402, 16332, 34]-code), using
  - constructionÂ X applied to C([0,16]) âŠ‚ C([0,13]) [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(128⁵³, 16385, F₁₂₈, 27) (dual of [16385, 16332, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 128⁴âˆ’1, defining interval IÂ =Â [0,13], and minimum distance dÂ â‰¥ |{−13,−12,…,13}|+1Â =Â 28 (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(128⁷⁰, 1412, F₁₂₈, 36, 33) (dual of [(1412, 36), 50762, 34]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row