MinT - Information on Result #1182682

Information on Result #1182682

Digital (223, 254, 4373)-net over F₂, using net defined by OOA based on linear OOA(2²⁵⁴, 4373, F₂, 31, 31) (dual of [(4373, 31), 135309, 32]-NRT-code), using

OOA 15-folding and stacking with additional row [i] based on linear OA(2²⁵⁴, 65596, F₂, 31) (dual of [65596, 65342, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(2²⁵⁴, 65597, F₂, 31) (dual of [65597, 65343, 32]-code), using
  - constructionÂ X applied to C_e(30) âŠ‚ C_e(24) [i] based on
    1. linear OA(2²⁴¹, 65536, F₂, 31) (dual of [65536, 65295, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 2¹⁶âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
    2. linear OA(2¹⁹³, 65536, F₂, 25) (dual of [65536, 65343, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 2¹⁶âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
    3. linear OA(2¹³, 61, F₂, 5) (dual of [61, 48, 6]-code), using
      - discarding factors / shortening the dual code based on linear OA(2¹³, 63, F₂, 5) (dual of [63, 50, 6]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 63Â = 2⁶âˆ’1, defining interval IÂ =Â [0,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [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, 254, 4373)-net over F₂	[i]		t-Expansion
2	Digital (224, 255, 4373)-net over F₂	[i]		Net Duplication