MinT - Information on Result #1131856

Information on Result #1131856

Linear OOA(2²¹⁷, 349533, F₂, 6, 20) (dual of [(349533, 6), 2096981, 21]-NRT-code), using OOA 6-folding based on linear OA(2²¹⁷, 2097198, F₂, 20) (dual of [2097198, 2096981, 21]-code), using

discarding factors / shortening the dual code based on linear OA(2²¹⁷, 2097201, F₂, 20) (dual of [2097201, 2096984, 21]-code), using
- 1 times truncation [i] based on linear OA(2²¹⁸, 2097202, F₂, 21) (dual of [2097202, 2096984, 22]-code), using
  - constructionÂ X applied to C([0,10]) âŠ‚ C([0,8]) [i] based on
    1. 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]
    2. linear OA(2¹⁶⁹, 2097153, F₂, 17) (dual of [2097153, 2096984, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153Â | 2⁴²âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (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, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Linear OOA(2²¹⁷, 349533, F₂, 7, 20) (dual of [(349533, 7), 2446514, 21]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²¹⁷, 349533, F₂, 8, 20) (dual of [(349533, 8), 2796047, 21]-NRT-code)	[i]
3	Digital (197, 217, 349533)-net over F₂	[i]