MinT - Information on Result #2486632

Information on Result #2486632

Linear OOA(3¹³⁶, 9859, F₃, 2, 22) (dual of [(9859, 2), 19582, 23]-NRT-code), using 3¹ times duplication based on linear OOA(3¹³⁵, 9859, F₃, 2, 22) (dual of [(9859, 2), 19583, 23]-NRT-code), using

OOA 2-folding [i] based on linear OA(3¹³⁵, 19718, F₃, 22) (dual of [19718, 19583, 23]-code), using
- constructionÂ X applied to C_e(21) âŠ‚ C_e(16) [i] based on
  1. 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]
  2. linear OA(3¹⁰⁰, 19683, F₃, 17) (dual of [19683, 19583, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
  3. linear OA(3⁸, 35, F₃, 4) (dual of [35, 27, 5]-code), using
    - discarding factors / shortening the dual code based on linear OA(3⁸, 41, F₃, 4) (dual of [41, 33, 5]-code), using
      - the narrow-sense BCH-code C(I) with length 41Â | 3⁸âˆ’1, defining interval IÂ =Â [1,1], and minimum distance dÂ â‰¥ |{−3,−1,1,3}|+1Â =Â 5 (BCH-bound) [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(3¹³⁶, 9168, F₃, 3, 22) (dual of [(9168, 3), 27368, 23]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3¹³⁶, 9168, F₃, 4, 22) (dual of [(9168, 4), 36536, 23]-NRT-code)	[i]
3	Linear OOA(3¹³⁶, 9168, F₃, 5, 22) (dual of [(9168, 5), 45704, 23]-NRT-code)	[i]
4	Digital (114, 136, 9168)-net over F₃	[i]