MinT - Information on Result #2668296

Information on Result #2668296

Linear OOA(2¹⁸⁸, 1375, F₂, 3, 31) (dual of [(1375, 3), 3937, 32]-NRT-code), using 2¹ times duplication based on linear OOA(2¹⁸⁷, 1375, F₂, 3, 31) (dual of [(1375, 3), 3938, 32]-NRT-code), using

OOA 3-folding [i] based on linear OA(2¹⁸⁷, 4125, F₂, 31) (dual of [4125, 3938, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(2¹⁸⁷, 4126, F₂, 31) (dual of [4126, 3939, 32]-code), using
  - constructionÂ X applied to C_e(30) âŠ‚ C_e(26) [i] based on
    1. linear OA(2¹⁸¹, 4096, F₂, 31) (dual of [4096, 3915, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
    2. 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]
    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(2¹⁸⁸, 1223, F₂, 4, 31) (dual of [(1223, 4), 4704, 32]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹⁸⁸, 1223, F₂, 5, 31) (dual of [(1223, 5), 5927, 32]-NRT-code)	[i]
3	Linear OOA(2¹⁸⁸, 1223, F₂, 6, 31) (dual of [(1223, 6), 7150, 32]-NRT-code)	[i]
4	Linear OOA(2¹⁸⁸, 1223, F₂, 7, 31) (dual of [(1223, 7), 8373, 32]-NRT-code)	[i]
5	Linear OOA(2¹⁸⁸, 1223, F₂, 8, 31) (dual of [(1223, 8), 9596, 32]-NRT-code)	[i]
6	Digital (157, 188, 1223)-net over F₂	[i]