MinT - Information on Result #1590988

Information on Result #1590988

Linear OOA(2¹²⁸, 1376, F₂, 4, 20) (dual of [(1376, 4), 5376, 21]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹²⁸, 1376, F₂, 3, 20) (dual of [(1376, 3), 4000, 21]-NRT-code), using

OOA 3-folding [i] based on linear OA(2¹²⁸, 4128, F₂, 20) (dual of [4128, 4000, 21]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2¹²⁶, 4126, F₂, 20) (dual of [4126, 4000, 21]-code), using
  - 1 times truncation [i] based on linear OA(2¹²⁷, 4127, F₂, 21) (dual of [4127, 4000, 22]-code), using
    - constructionÂ X applied to C([0,10]) âŠ‚ C([0,8]) [i] based on
      1. linear OA(2¹²¹, 4097, F₂, 21) (dual of [4097, 3976, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097Â | 2²⁴âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]
      2. linear OA(2⁹⁷, 4097, F₂, 17) (dual of [4097, 4000, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097Â | 2²⁴âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]
      3. linear OA(2⁶, 30, F₂, 3) (dual of [30, 24, 4]-code or 30-cap in PG(5,2)), using
        discarding factors / shortening the dual code based on linear OA(2⁶, 32, F₂, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
        Reedâ€“Muller code RM(1,5) [i]
        caps in base bÂ =Â 2 [i]

Mode: 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		This result only	Method
1	Linear OOA(2¹²⁹, 1376, F₂, 4, 20) (dual of [(1376, 4), 5375, 21]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(2¹²⁸, 688, F₂, 7, 20) (dual of [(688, 7), 4688, 21]-NRT-code)	[i]		OOA Folding
3	Linear OOA(2¹²⁸, 688, F₂, 8, 20) (dual of [(688, 8), 5376, 21]-NRT-code)	[i]		OOA Folding