MinT - Information on Result #1188024

Information on Result #1188024

Digital (212, 253, 3279)-net over F₄, using net defined by OOA based on linear OOA(4²⁵³, 3279, F₄, 41, 41) (dual of [(3279, 41), 134186, 42]-NRT-code), using

OOA 20-folding and stacking with additional row [i] based on linear OA(4²⁵³, 65581, F₄, 41) (dual of [65581, 65328, 42]-code), using
- 2 times code embedding in larger space [i] based on linear OA(4²⁵¹, 65579, F₄, 41) (dual of [65579, 65328, 42]-code), using
  - constructionÂ X applied to C([0,20]) âŠ‚ C([0,17]) [i] based on
    1. linear OA(4²⁴¹, 65537, F₄, 41) (dual of [65537, 65296, 42]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 4¹⁶âˆ’1, defining interval IÂ =Â [0,20], and minimum distance dÂ â‰¥ |{−20,−19,…,20}|+1Â =Â 42 (BCH-bound) [i]
    2. linear OA(4²⁰⁹, 65537, F₄, 35) (dual of [65537, 65328, 36]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 4¹⁶âˆ’1, defining interval IÂ =Â [0,17], and minimum distance dÂ â‰¥ |{−17,−16,…,17}|+1Â =Â 36 (BCH-bound) [i]
    3. linear OA(4¹⁰, 42, F₄, 5) (dual of [42, 32, 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 (213, 253, 3279)-net over F₄	[i]	t-Expansion
2	Digital (213, 254, 3279)-net over F₄	[i]	Net Duplication
3	Digital (214, 255, 3279)-net over F₄	[i]
4	Digital (215, 256, 3279)-net over F₄	[i]
5	Digital (212, 252, 3279)-net over F₄	[i]	m-Reduction