MinT - Information on Result #1192776

Information on Result #1192776

Digital (142, 169, 161322)-net over F₈, using net defined by OOA based on linear OOA(8¹⁶⁹, 161322, F₈, 27, 27) (dual of [(161322, 27), 4355525, 28]-NRT-code), using

OOA 13-folding and stacking with additional row [i] based on linear OA(8¹⁶⁹, 2097187, F₈, 27) (dual of [2097187, 2097018, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(8¹⁶⁹, 2097194, F₈, 27) (dual of [2097194, 2097025, 28]-code), using
  - constructionÂ X applied to C_e(26) âŠ‚ C_e(20) [i] based on
    1. linear OA(8¹⁶², 2097152, F₈, 27) (dual of [2097152, 2096990, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 8⁷âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
    2. linear OA(8¹²⁷, 2097152, F₈, 21) (dual of [2097152, 2097025, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 8⁷âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
    3. linear OA(8⁷, 42, F₈, 5) (dual of [42, 35, 6]-code), using
      - discarding factors / shortening the dual code based on linear OA(8⁷, 57, F₈, 5) (dual of [57, 50, 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 (143, 170, 161322)-net over F₈	[i]	Net Duplication
2	Digital (144, 171, 161322)-net over F₈	[i]
3	Digital (145, 172, 161322)-net over F₈	[i]