MinT - Information on Result #1195704

Information on Result #1195704

Digital (89, 116, 10085)-net over F₁₆, using net defined by OOA based on linear OOA(16¹¹⁶, 10085, F₁₆, 27, 27) (dual of [(10085, 27), 272179, 28]-NRT-code), using

OOA 13-folding and stacking with additional row [i] based on linear OA(16¹¹⁶, 131106, F₁₆, 27) (dual of [131106, 130990, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(16¹¹⁶, 131108, F₁₆, 27) (dual of [131108, 130992, 28]-code), using
  - trace code [i] based on linear OA(256⁵⁸, 65554, F₂₅₆, 27) (dual of [65554, 65496, 28]-code), using
    - constructionÂ X applied to C([0,13]) âŠ‚ C([0,10]) [i] based on
      1. linear OA(256⁵³, 65537, F₂₅₆, 27) (dual of [65537, 65484, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,13], and minimum distance dÂ â‰¥ |{−13,−12,…,13}|+1Â =Â 28 (BCH-bound) [i]
      2. linear OA(256⁴¹, 65537, F₂₅₆, 21) (dual of [65537, 65496, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]
      3. linear OA(256⁵, 17, F₂₅₆, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,256)), using
        discarding factors / shortening the dual code based on linear OA(256⁵, 256, F₂₅₆, 5) (dual of [256, 251, 6]-code or 256-arc in PG(4,256)), using
        Reedâ€“Solomon code RS(251,256) [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	Digital (90, 117, 10085)-net over F₁₆	[i]		Net Duplication
2	Digital (91, 118, 10085)-net over F₁₆	[i]		Net Duplication