MinT - Information on Result #1131459

Information on Result #1131459

Linear OOA(2¹⁶⁸, 174770, F₂, 6, 17) (dual of [(174770, 6), 1048452, 18]-NRT-code), using OOA 6-folding based on linear OA(2¹⁶⁸, 1048620, F₂, 17) (dual of [1048620, 1048452, 18]-code), using

discarding factors / shortening the dual code based on linear OA(2¹⁶⁸, 1048624, F₂, 17) (dual of [1048624, 1048456, 18]-code), using
- constructionÂ X applied to C([0,8]) âŠ‚ C([0,6]) [i] based on
  1. linear OA(2¹⁶¹, 1048577, F₂, 17) (dual of [1048577, 1048416, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577Â | 2⁴⁰âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]
  2. linear OA(2¹²¹, 1048577, F₂, 13) (dual of [1048577, 1048456, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577Â | 2⁴⁰âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]
  3. linear OA(2⁷, 47, F₂, 3) (dual of [47, 40, 4]-code or 47-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(2¹⁶⁸, 174770, F₂, 7, 17) (dual of [(174770, 7), 1223222, 18]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹⁶⁸, 174770, F₂, 8, 17) (dual of [(174770, 8), 1397992, 18]-NRT-code)	[i]
3	Digital (151, 168, 174770)-net over F₂	[i]