MinT - Information on Result #1131848

Information on Result #1131848

Linear OOA(2¹⁹⁸, 87389, F₂, 6, 20) (dual of [(87389, 6), 524136, 21]-NRT-code), using OOA 6-folding based on linear OA(2¹⁹⁸, 524334, F₂, 20) (dual of [524334, 524136, 21]-code), using

strength reduction [i] based on linear OA(2¹⁹⁸, 524334, F₂, 21) (dual of [524334, 524136, 22]-code), using
- constructionÂ X applied to C([0,10]) âŠ‚ C([0,8]) [i] based on
  1. linear OA(2¹⁹¹, 524289, F₂, 21) (dual of [524289, 524098, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 524289Â | 2³⁸âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]
  2. linear OA(2¹⁵³, 524289, F₂, 17) (dual of [524289, 524136, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 524289Â | 2³⁸âˆ’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, 45, F₂, 3) (dual of [45, 38, 4]-code or 45-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(2¹⁹⁹, 87389, F₂, 6, 20) (dual of [(87389, 6), 524135, 21]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2¹⁹⁸, 87389, F₂, 7, 20) (dual of [(87389, 7), 611525, 21]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
3	Linear OOA(2¹⁹⁸, 87389, F₂, 8, 20) (dual of [(87389, 8), 698914, 21]-NRT-code)	[i]
4	Digital (178, 198, 87389)-net over F₂	[i]