MinT - Information on Result #2627346

Information on Result #2627346

Linear OOA(3²²¹, 177156, F₃, 3, 27) (dual of [(177156, 3), 531247, 28]-NRT-code), using strength reduction based on linear OOA(3²²¹, 177156, F₃, 3, 28) (dual of [(177156, 3), 531247, 29]-NRT-code), using

OOA 3-folding [i] based on linear OA(3²²¹, 531468, F₃, 28) (dual of [531468, 531247, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(3²²¹, 531469, F₃, 28) (dual of [531469, 531248, 29]-code), using
  - constructionÂ X applied to C_e(27) âŠ‚ C_e(24) [i] based on
    1. linear OA(3²¹⁷, 531441, F₃, 28) (dual of [531441, 531224, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
    2. linear OA(3¹⁹³, 531441, F₃, 25) (dual of [531441, 531248, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
    3. linear OA(3⁴, 28, F₃, 2) (dual of [28, 24, 3]-code), using
      - discarding factors / shortening the dual code based on linear OA(3⁴, 40, F₃, 2) (dual of [40, 36, 3]-code), using
        Hamming code H(4,3) [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(3²²¹, 156908, F₃, 4, 27) (dual of [(156908, 4), 627411, 28]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3²²¹, 156908, F₃, 5, 27) (dual of [(156908, 5), 784319, 28]-NRT-code)	[i]
3	Digital (194, 221, 156908)-net over F₃	[i]