MinT - Information on Result #2668083

Information on Result #2668083

Linear OOA(2¹⁷⁸, 1376, F₂, 3, 29) (dual of [(1376, 3), 3950, 30]-NRT-code), using 2² times duplication based on linear OOA(2¹⁷⁶, 1376, F₂, 3, 29) (dual of [(1376, 3), 3952, 30]-NRT-code), using

OOA 3-folding [i] based on linear OA(2¹⁷⁶, 4128, F₂, 29) (dual of [4128, 3952, 30]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2¹⁷⁵, 4127, F₂, 29) (dual of [4127, 3952, 30]-code), using
  - constructionÂ X applied to C([0,14]) âŠ‚ C([0,12]) [i] based on
    1. linear OA(2¹⁶⁹, 4097, F₂, 29) (dual of [4097, 3928, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097Â | 2²⁴âˆ’1, defining interval IÂ =Â [0,14], and minimum distance dÂ â‰¥ |{−14,−13,…,14}|+1Â =Â 30 (BCH-bound) [i]
    2. linear OA(2¹⁴⁵, 4097, F₂, 25) (dual of [4097, 3952, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097Â | 2²⁴âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (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: 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(2¹⁷⁸, 1267, F₂, 4, 29) (dual of [(1267, 4), 4890, 30]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹⁷⁸, 1267, F₂, 5, 29) (dual of [(1267, 5), 6157, 30]-NRT-code)	[i]
3	Linear OOA(2¹⁷⁸, 1267, F₂, 6, 29) (dual of [(1267, 6), 7424, 30]-NRT-code)	[i]
4	Linear OOA(2¹⁷⁸, 1267, F₂, 7, 29) (dual of [(1267, 7), 8691, 30]-NRT-code)	[i]
5	Linear OOA(2¹⁷⁸, 1267, F₂, 8, 29) (dual of [(1267, 8), 9958, 30]-NRT-code)	[i]
6	Digital (149, 178, 1267)-net over F₂	[i]