MinT - Information on Result #2487010

Information on Result #2487010

Linear OOA(3¹⁶³, 9859, F₃, 2, 26) (dual of [(9859, 2), 19555, 27]-NRT-code), using 3¹ times duplication based on linear OOA(3¹⁶², 9859, F₃, 2, 26) (dual of [(9859, 2), 19556, 27]-NRT-code), using

1 times NRT-code embedding in larger space [i] based on linear OOA(3¹⁶⁰, 9858, F₃, 2, 26) (dual of [(9858, 2), 19556, 27]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3¹⁶⁰, 19716, F₃, 26) (dual of [19716, 19556, 27]-code), using
  - constructionÂ X applied to C_e(25) âŠ‚ C_e(21) [i] based on
    1. linear OA(3¹⁵⁴, 19683, F₃, 26) (dual of [19683, 19529, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
    2. linear OA(3¹²⁷, 19683, F₃, 22) (dual of [19683, 19556, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
    3. linear OA(3⁶, 33, F₃, 3) (dual of [33, 27, 4]-code or 33-cap in PG(5,3)), using
      - discarding factors / shortening the dual code based on linear OA(3⁶, 48, F₃, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
        large caps in PG(5,Â b) [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Linear OOA(3¹⁶³, 9859, F₃, 3, 26) (dual of [(9859, 3), 29414, 27]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3¹⁶³, 9859, F₃, 4, 26) (dual of [(9859, 4), 39273, 27]-NRT-code)	[i]
3	Linear OOA(3¹⁶³, 9859, F₃, 5, 26) (dual of [(9859, 5), 49132, 27]-NRT-code)	[i]
4	Digital (137, 163, 9859)-net over F₃	[i]