MinT - Information on Result #1182384

Information on Result #1182384

Digital (235, 260, 174766)-net over F₂, using net defined by OOA based on linear OOA(2²⁶⁰, 174766, F₂, 25, 25) (dual of [(174766, 25), 4368890, 26]-NRT-code), using

OOA 12-folding and stacking with additional row [i] based on linear OA(2²⁶⁰, 2097193, F₂, 25) (dual of [2097193, 2096933, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(2²⁶⁰, 2097202, F₂, 25) (dual of [2097202, 2096942, 26]-code), using
  - constructionÂ X applied to C([0,12]) âŠ‚ C([0,10]) [i] based on
    1. linear OA(2²⁵³, 2097153, F₂, 25) (dual of [2097153, 2096900, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153Â | 2⁴²âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
    2. linear OA(2²¹¹, 2097153, F₂, 21) (dual of [2097153, 2096942, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153Â | 2⁴²âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]
    3. linear OA(2⁷, 49, F₂, 3) (dual of [49, 42, 4]-code or 49-cap in PG(6,2)), using
      - discarding factors / shortening the dual code based on linear OA(2⁷, 63, F₂, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 63Â = 2⁶âˆ’1, defining interval IÂ =Â [0,1], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [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 (236, 260, 174766)-net over F₂	[i]		t-Expansion