MinT - Information on Result #2789462

Information on Result #2789462

Linear OOA(2¹⁸⁷, 4100, F₂, 4, 26) (dual of [(4100, 4), 16213, 27]-NRT-code), using 2² times duplication based on linear OOA(2¹⁸⁵, 4100, F₂, 4, 26) (dual of [(4100, 4), 16215, 27]-NRT-code), using

OOA 4-folding [i] based on linear OA(2¹⁸⁵, 16400, F₂, 26) (dual of [16400, 16215, 27]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2¹⁸³, 16398, F₂, 26) (dual of [16398, 16215, 27]-code), using
  - 1 times truncation [i] based on linear OA(2¹⁸⁴, 16399, F₂, 27) (dual of [16399, 16215, 28]-code), using
    - constructionÂ X applied to C_e(26) âŠ‚ C_e(24) [i] based on
      1. linear OA(2¹⁸³, 16384, F₂, 27) (dual of [16384, 16201, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 2¹⁴âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
      2. linear OA(2¹⁶⁹, 16384, F₂, 25) (dual of [16384, 16215, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 2¹⁴âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
      3. linear OA(2¹, 15, F₂, 1) (dual of [15, 14, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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(2¹⁸⁷, 3615, F₂, 5, 26) (dual of [(3615, 5), 17888, 27]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹⁸⁷, 3615, F₂, 6, 26) (dual of [(3615, 6), 21503, 27]-NRT-code)	[i]
3	Linear OOA(2¹⁸⁷, 3615, F₂, 7, 26) (dual of [(3615, 7), 25118, 27]-NRT-code)	[i]
4	Linear OOA(2¹⁸⁷, 3615, F₂, 8, 26) (dual of [(3615, 8), 28733, 27]-NRT-code)	[i]
5	Digital (161, 187, 3615)-net over F₂	[i]