MinT - Information on Result #3185585

Information on Result #3185585

Digital (158, 184, 1261)-net over F₂, using t-expansion based on digital (157, 184, 1261)-net over F₂, using

net defined by OOA [i] based on linear OOA(2¹⁸⁴, 1261, F₂, 27, 27) (dual of [(1261, 27), 33863, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(2¹⁸⁴, 16394, F₂, 27) (dual of [16394, 16210, 28]-code), using
  - discarding factors / shortening the dual code 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, 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 (159, 185, 1261)-net over F₂	[i]		Net Duplication
2	Digital (160, 186, 1261)-net over F₂	[i]
3	Digital (161, 187, 1261)-net over F₂	[i]