MinT - Information on Result #2677458

Information on Result #2677458

Linear OOA(3¹⁷⁶, 177157, F₃, 3, 22) (dual of [(177157, 3), 531295, 23]-NRT-code), using 3¹ times duplication based on linear OOA(3¹⁷⁵, 177157, F₃, 3, 22) (dual of [(177157, 3), 531296, 23]-NRT-code), using

OOA 3-folding [i] based on linear OA(3¹⁷⁵, 531471, F₃, 22) (dual of [531471, 531296, 23]-code), using
- 2 times code embedding in larger space [i] based on linear OA(3¹⁷³, 531469, F₃, 22) (dual of [531469, 531296, 23]-code), using
  - constructionÂ X applied to C_e(21) âŠ‚ C_e(18) [i] based on
    1. linear OA(3¹⁶⁹, 531441, F₃, 22) (dual of [531441, 531272, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
    2. linear OA(3¹⁴⁵, 531441, F₃, 19) (dual of [531441, 531296, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [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(3¹⁷⁶, 145450, F₃, 4, 22) (dual of [(145450, 4), 581624, 23]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3¹⁷⁶, 145450, F₃, 5, 22) (dual of [(145450, 5), 727074, 23]-NRT-code)	[i]
3	Digital (154, 176, 145450)-net over F₃	[i]