MinT - Information on Result #2668928

Information on Result #2668928

Linear OOA(2²²⁶, 1376, F₂, 3, 37) (dual of [(1376, 3), 3902, 38]-NRT-code), using 2² times duplication based on linear OOA(2²²⁴, 1376, F₂, 3, 37) (dual of [(1376, 3), 3904, 38]-NRT-code), using

OOA 3-folding [i] based on linear OA(2²²⁴, 4128, F₂, 37) (dual of [4128, 3904, 38]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2²²³, 4127, F₂, 37) (dual of [4127, 3904, 38]-code), using
  - constructionÂ X applied to C([0,18]) âŠ‚ C([0,16]) [i] based on
    1. linear OA(2²¹⁷, 4097, F₂, 37) (dual of [4097, 3880, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097Â | 2²⁴âˆ’1, defining interval IÂ =Â [0,18], and minimum distance dÂ â‰¥ |{−18,−17,…,18}|+1Â =Â 38 (BCH-bound) [i]
    2. linear OA(2¹⁹³, 4097, F₂, 33) (dual of [4097, 3904, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097Â | 2²⁴âˆ’1, defining interval IÂ =Â [0,16], and minimum distance dÂ â‰¥ |{−16,−15,…,16}|+1Â =Â 34 (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(2²²⁶, 1376, F₂, 4, 37) (dual of [(1376, 4), 5278, 38]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²²⁶, 1376, F₂, 5, 37) (dual of [(1376, 5), 6654, 38]-NRT-code)	[i]
3	Linear OOA(2²²⁶, 1376, F₂, 6, 37) (dual of [(1376, 6), 8030, 38]-NRT-code)	[i]
4	Linear OOA(2²²⁶, 1376, F₂, 7, 37) (dual of [(1376, 7), 9406, 38]-NRT-code)	[i]
5	Linear OOA(2²²⁶, 1376, F₂, 8, 37) (dual of [(1376, 8), 10782, 38]-NRT-code)	[i]
6	Digital (189, 226, 1376)-net over F₂	[i]