MinT - Information on Result #3188167

Information on Result #3188167

Digital (184, 212, 2341)-net over F₂, using t-expansion based on digital (183, 212, 2341)-net over F₂, using

net defined by OOA [i] based on linear OOA(2²¹², 2341, F₂, 29, 29) (dual of [(2341, 29), 67677, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(2²¹², 32775, F₂, 29) (dual of [32775, 32563, 30]-code), using
  - discarding factors / shortening the dual code based on linear OA(2²¹², 32784, F₂, 29) (dual of [32784, 32572, 30]-code), using
    - constructionÂ X applied to C_e(28) âŠ‚ C_e(26) [i] based on
      1. linear OA(2²¹¹, 32768, F₂, 29) (dual of [32768, 32557, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 2¹⁵âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
      2. linear OA(2¹⁹⁶, 32768, F₂, 27) (dual of [32768, 32572, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 2¹⁵âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
      3. linear OA(2¹, 16, F₂, 1) (dual of [16, 15, 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, k and s, k and t, m and s, m and t, t and s.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Digital (185, 213, 2341)-net over F₂	[i]		Net Duplication
2	Digital (186, 214, 2341)-net over F₂	[i]
3	Digital (187, 215, 2341)-net over F₂	[i]