MinT - Information on Result #1195692

Information on Result #1195692

Digital (101, 127, 80662)-net over F₁₆, using net defined by OOA based on linear OOA(16¹²⁷, 80662, F₁₆, 26, 26) (dual of [(80662, 26), 2097085, 27]-NRT-code), using

OA 13-folding and stacking [i] based on linear OA(16¹²⁷, 1048606, F₁₆, 26) (dual of [1048606, 1048479, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(16¹²⁷, 1048607, F₁₆, 26) (dual of [1048607, 1048480, 27]-code), using
  - constructionÂ X applied to C_e(25) âŠ‚ C_e(20) [i] based on
    1. linear OA(16¹²¹, 1048576, F₁₆, 26) (dual of [1048576, 1048455, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 16⁵âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
    2. linear OA(16⁹⁶, 1048576, F₁₆, 21) (dual of [1048576, 1048480, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 16⁵âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
    3. linear OA(16⁶, 31, F₁₆, 4) (dual of [31, 25, 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 (102, 128, 80662)-net over F₁₆	[i]	Net Duplication
2	Digital (103, 129, 80662)-net over F₁₆	[i]
3	Digital (104, 130, 80662)-net over F₁₆	[i]