MinT - Information on Result #952850

Information on Result #952850

Linear OOA(3¹⁴⁹, 177156, F₃, 3, 19) (dual of [(177156, 3), 531319, 20]-NRT-code), using OOA 3-folding based on linear OA(3¹⁴⁹, 531468, F₃, 19) (dual of [531468, 531319, 20]-code), using

discarding factors / shortening the dual code based on linear OA(3¹⁴⁹, 531469, F₃, 19) (dual of [531469, 531320, 20]-code), using
- constructionÂ X applied to C_e(18) âŠ‚ C_e(15) [i] based on
  1. 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]
  2. linear OA(3¹²¹, 531441, F₃, 16) (dual of [531441, 531320, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [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(3¹⁴⁹, 177156, F₃, 3, 18) (dual of [(177156, 3), 531319, 19]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(3¹⁵⁰, 177156, F₃, 3, 19) (dual of [(177156, 3), 531318, 20]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(3¹⁴⁹, 141473, F₃, 4, 19) (dual of [(141473, 4), 565743, 20]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
4	Linear OOA(3¹⁴⁹, 141473, F₃, 5, 19) (dual of [(141473, 5), 707216, 20]-NRT-code)	[i]
5	Digital (130, 149, 141473)-net over F₃	[i]