MinT - Information on Result #1180502

Information on Result #1180502

Digital (115, 128, 349529)-net over F₂, using net defined by OOA based on linear OOA(2¹²⁸, 349529, F₂, 13, 13) (dual of [(349529, 13), 4543749, 14]-NRT-code), using

OOA 6-folding and stacking with additional row [i] based on linear OA(2¹²⁸, 2097175, F₂, 13) (dual of [2097175, 2097047, 14]-code), using
- constructionÂ X4 applied to C_e(12) âŠ‚ C_e(10) [i] based on
  1. linear OA(2¹²⁷, 2097152, F₂, 13) (dual of [2097152, 2097025, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 2²¹âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
  2. linear OA(2¹⁰⁶, 2097152, F₂, 11) (dual of [2097152, 2097046, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 2²¹âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
  3. linear OA(2²², 23, F₂, 21) (dual of [23, 1, 22]-code), using
    - strength reduction [i] based on linear OA(2²², 23, F₂, 22) (dual of [23, 1, 23]-code or 23-arc in PG(21,2)), using
      - dual of repetition code with length 23 [i]
  4. linear OA(2¹, 23, F₂, 1) (dual of [23, 22, 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		Method
1	Digital (116, 128, 349529)-net over F₂	[i]	t-Expansion
2	Digital (116, 129, 349529)-net over F₂	[i]	Net Duplication
3	Digital (117, 130, 349529)-net over F₂	[i]
4	Digital (118, 131, 349529)-net over F₂	[i]
5	Digital (119, 132, 349529)-net over F₂	[i]