MinT - Information on Result #2789771

Information on Result #2789771

Linear OOA(2²⁰⁷, 4105, F₂, 4, 29) (dual of [(4105, 4), 16213, 30]-NRT-code), using 2³ times duplication based on linear OOA(2²⁰⁴, 4105, F₂, 4, 29) (dual of [(4105, 4), 16216, 30]-NRT-code), using

OOA 4-folding [i] based on linear OA(2²⁰⁴, 16420, F₂, 29) (dual of [16420, 16216, 30]-code), using
- constructionÂ X applied to C([0,14]) âŠ‚ C([0,12]) [i] based on
  1. linear OA(2¹⁹⁷, 16385, F₂, 29) (dual of [16385, 16188, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 2²⁸âˆ’1, defining interval IÂ =Â [0,14], and minimum distance dÂ â‰¥ |{−14,−13,…,14}|+1Â =Â 30 (BCH-bound) [i]
  2. linear OA(2¹⁶⁹, 16385, F₂, 25) (dual of [16385, 16216, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 2²⁸âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
  3. linear OA(2⁷, 35, F₂, 3) (dual of [35, 28, 4]-code or 35-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(2²⁰⁷, 3413, F₂, 5, 29) (dual of [(3413, 5), 16858, 30]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²⁰⁷, 3413, F₂, 6, 29) (dual of [(3413, 6), 20271, 30]-NRT-code)	[i]
3	Linear OOA(2²⁰⁷, 3413, F₂, 7, 29) (dual of [(3413, 7), 23684, 30]-NRT-code)	[i]
4	Linear OOA(2²⁰⁷, 3413, F₂, 8, 29) (dual of [(3413, 8), 27097, 30]-NRT-code)	[i]
5	Digital (178, 207, 3413)-net over F₂	[i]