MinT - Information on Result #2667876

Information on Result #2667876

Linear OOA(2¹⁶⁸, 1377, F₂, 3, 27) (dual of [(1377, 3), 3963, 28]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(2¹⁶⁵, 1376, F₂, 3, 27) (dual of [(1376, 3), 3963, 28]-NRT-code), using

OOA 3-folding [i] based on linear OA(2¹⁶⁵, 4128, F₂, 27) (dual of [4128, 3963, 28]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2¹⁶³, 4126, F₂, 27) (dual of [4126, 3963, 28]-code), using
  - constructionÂ X applied to C_e(26) âŠ‚ C_e(22) [i] based on
    1. linear OA(2¹⁵⁷, 4096, F₂, 27) (dual of [4096, 3939, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
    2. linear OA(2¹³³, 4096, F₂, 23) (dual of [4096, 3963, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [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(2¹⁶⁸, 1328, F₂, 4, 27) (dual of [(1328, 4), 5144, 28]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹⁶⁸, 1328, F₂, 5, 27) (dual of [(1328, 5), 6472, 28]-NRT-code)	[i]
3	Linear OOA(2¹⁶⁸, 1328, F₂, 6, 27) (dual of [(1328, 6), 7800, 28]-NRT-code)	[i]
4	Linear OOA(2¹⁶⁸, 1328, F₂, 7, 27) (dual of [(1328, 7), 9128, 28]-NRT-code)	[i]
5	Linear OOA(2¹⁶⁸, 1328, F₂, 8, 27) (dual of [(1328, 8), 10456, 28]-NRT-code)	[i]
6	Digital (141, 168, 1328)-net over F₂	[i]