MinT - Information on Result #3193292

Information on Result #3193292

Digital (223, 257, 1928)-net over F₂, using t-expansion based on digital (222, 257, 1928)-net over F₂, using

net defined by OOA [i] based on linear OOA(2²⁵⁷, 1928, F₂, 35, 35) (dual of [(1928, 35), 67223, 36]-NRT-code), using
- OOA 17-folding and stacking with additional row [i] based on linear OA(2²⁵⁷, 32777, F₂, 35) (dual of [32777, 32520, 36]-code), using
  - discarding factors / shortening the dual code based on linear OA(2²⁵⁷, 32784, F₂, 35) (dual of [32784, 32527, 36]-code), using
    - constructionÂ X applied to C_e(34) âŠ‚ C_e(32) [i] based on
      1. linear OA(2²⁵⁶, 32768, F₂, 35) (dual of [32768, 32512, 36]-code), using an extension C_e(34) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 2¹⁵âˆ’1, defining interval IÂ =Â [1,34], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 35 [i]
      2. linear OA(2²⁴¹, 32768, F₂, 33) (dual of [32768, 32527, 34]-code), using an extension C_e(32) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 2¹⁵âˆ’1, defining interval IÂ =Â [1,32], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 33 [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 (224, 258, 1928)-net over F₂	[i]		Net Duplication
2	Digital (225, 259, 1928)-net over F₂	[i]
3	Digital (226, 260, 1928)-net over F₂	[i]