MinT - Information on Result #1187928

Information on Result #1187928

Digital (210, 245, 15423)-net over F₄, using net defined by OOA based on linear OOA(4²⁴⁵, 15423, F₄, 35, 35) (dual of [(15423, 35), 539560, 36]-NRT-code), using

OOA 17-folding and stacking with additional row [i] based on linear OA(4²⁴⁵, 262192, F₄, 35) (dual of [262192, 261947, 36]-code), using
- discarding factors / shortening the dual code based on linear OA(4²⁴⁵, 262199, F₄, 35) (dual of [262199, 261954, 36]-code), using
  - constructionÂ X applied to C_e(34) âŠ‚ C_e(28) [i] based on
    1. linear OA(4²³⁵, 262144, F₄, 35) (dual of [262144, 261909, 36]-code), using an extension C_e(34) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,34], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 35 [i]
    2. linear OA(4¹⁹⁰, 262144, F₄, 29) (dual of [262144, 261954, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
    3. linear OA(4¹⁰, 55, F₄, 5) (dual of [55, 45, 6]-code), using
      - discarding factors / shortening the dual code based on linear OA(4¹⁰, 63, F₄, 5) (dual of [63, 53, 6]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 63Â = 4³âˆ’1, defining interval IÂ =Â [0,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [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		Method
1	Digital (211, 246, 15423)-net over F₄	[i]	Net Duplication
2	Digital (212, 247, 15423)-net over F₄	[i]
3	Digital (213, 248, 15423)-net over F₄	[i]
4	Digital (214, 249, 15423)-net over F₄	[i]
5	Digital (215, 250, 15423)-net over F₄	[i]