MinT - Information on Result #1052116

Information on Result #1052116

Linear OOA(2¹²⁷, 4099, F₂, 4, 18) (dual of [(4099, 4), 16269, 19]-NRT-code), using OOA 4-folding based on linear OA(2¹²⁷, 16396, F₂, 18) (dual of [16396, 16269, 19]-code), using

discarding factors / shortening the dual code based on linear OA(2¹²⁷, 16398, F₂, 18) (dual of [16398, 16271, 19]-code), using
- 1 times truncation [i] based on linear OA(2¹²⁸, 16399, F₂, 19) (dual of [16399, 16271, 20]-code), using
  - constructionÂ X applied to C_e(18) âŠ‚ C_e(16) [i] based on
    1. linear OA(2¹²⁷, 16384, F₂, 19) (dual of [16384, 16257, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 2¹⁴âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
    2. linear OA(2¹¹³, 16384, F₂, 17) (dual of [16384, 16271, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 2¹⁴âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [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(2¹²⁷, 3977, F₂, 5, 18) (dual of [(3977, 5), 19758, 19]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹²⁷, 3977, F₂, 6, 18) (dual of [(3977, 6), 23735, 19]-NRT-code)	[i]
3	Linear OOA(2¹²⁷, 3977, F₂, 7, 18) (dual of [(3977, 7), 27712, 19]-NRT-code)	[i]
4	Linear OOA(2¹²⁷, 3977, F₂, 8, 18) (dual of [(3977, 8), 31689, 19]-NRT-code)	[i]
5	Digital (109, 127, 3977)-net over F₂	[i]