MinT - Information on Result #1191390

Information on Result #1191390

Digital (37, 48, 6556)-net over F₈, using net defined by OOA based on linear OOA(8⁴⁸, 6556, F₈, 11, 11) (dual of [(6556, 11), 72068, 12]-NRT-code), using

OOA 5-folding and stacking with additional row [i] based on linear OA(8⁴⁸, 32781, F₈, 11) (dual of [32781, 32733, 12]-code), using
- 1 times code embedding in larger space [i] based on linear OA(8⁴⁷, 32780, F₈, 11) (dual of [32780, 32733, 12]-code), using
  - constructionÂ X4 applied to C_e(10) âŠ‚ C_e(8) [i] based on
    1. linear OA(8⁴⁶, 32768, F₈, 11) (dual of [32768, 32722, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
    2. linear OA(8³⁶, 32768, F₈, 9) (dual of [32768, 32732, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
    3. linear OA(8¹¹, 12, F₈, 11) (dual of [12, 1, 12]-code or 12-arc in PG(10,8)), using
      - dual of repetition code with length 12 [i]
    4. linear OA(8¹, 12, F₈, 1) (dual of [12, 11, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(8¹, 511, F₈, 1) (dual of [511, 510, 2]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 511Â = 8³âˆ’1, defining interval IÂ =Â [0,0], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 2 [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 (38, 49, 6556)-net over F₈	[i]		Net Duplication