MinT - Information on Result #2677278

Information on Result #2677278

Linear OOA(3¹⁶², 177156, F₃, 3, 20) (dual of [(177156, 3), 531306, 21]-NRT-code), using 3¹ times duplication based on linear OOA(3¹⁶¹, 177156, F₃, 3, 20) (dual of [(177156, 3), 531307, 21]-NRT-code), using

OOA 3-folding [i] based on linear OA(3¹⁶¹, 531468, F₃, 20) (dual of [531468, 531307, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(3¹⁶¹, 531469, F₃, 20) (dual of [531469, 531308, 21]-code), using
  - constructionÂ X applied to C_e(19) âŠ‚ C_e(16) [i] based on
    1. linear OA(3¹⁵⁷, 531441, F₃, 20) (dual of [531441, 531284, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
    2. linear OA(3¹³³, 531441, F₃, 17) (dual of [531441, 531308, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [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(3¹⁶², 177156, F₃, 4, 20) (dual of [(177156, 4), 708462, 21]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3¹⁶², 177156, F₃, 5, 20) (dual of [(177156, 5), 885618, 21]-NRT-code)	[i]
3	Digital (142, 162, 177156)-net over F₃	[i]