MinT - Information on Result #3267826

Information on Result #3267826

Digital (39, 72, 1025)-net over F₁₂₈, using 128² times duplication based on digital (37, 70, 1025)-net over F₁₂₈, using

net defined by OOA [i] based on linear OOA(128⁷⁰, 1025, F₁₂₈, 33, 33) (dual of [(1025, 33), 33755, 34]-NRT-code), using
- OOA 16-folding and stacking with additional row [i] based on linear OA(128⁷⁰, 16401, F₁₂₈, 33) (dual of [16401, 16331, 34]-code), using
  - discarding factors / shortening the dual code 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: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	(51, 84, 1025)-net in base 64	[i]		Base Change