MinT - Information on Result #1195360

Information on Result #1195360

Digital (65, 82, 131075)-net over F₁₆, using net defined by OOA based on linear OOA(16⁸², 131075, F₁₆, 17, 17) (dual of [(131075, 17), 2228193, 18]-NRT-code), using

OOA 8-folding and stacking with additional row [i] based on linear OA(16⁸², 1048601, F₁₆, 17) (dual of [1048601, 1048519, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(16⁸², 1048602, F₁₆, 17) (dual of [1048602, 1048520, 18]-code), using
  - constructionÂ X applied to C_e(16) âŠ‚ C_e(11) [i] based on
    1. linear OA(16⁷⁶, 1048576, F₁₆, 17) (dual of [1048576, 1048500, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 16⁵âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
    2. linear OA(16⁵⁶, 1048576, F₁₆, 12) (dual of [1048576, 1048520, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 16⁵âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
    3. linear OA(16⁶, 26, F₁₆, 4) (dual of [26, 20, 5]-code), using
      - discarding factors / shortening the dual code based on linear OA(16⁶, 240, F₁₆, 4) (dual of [240, 234, 5]-code), using
        1 times truncation [i] based on linear OA(16⁷, 241, F₁₆, 5) (dual of [241, 234, 6]-code), using
        a code by Danev and Olsson [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 (66, 82, 131075)-net over F₁₆	[i]	t-Expansion
2	Digital (66, 83, 131075)-net over F₁₆	[i]	Net Duplication
3	Digital (65, 81, 131075)-net over F₁₆	[i]	m-Reduction