MinT - Information on Result #1100914

Information on Result #1100914

Linear OOA(3¹¹⁷, 956600, F₃, 5, 13) (dual of [(956600, 5), 4782883, 14]-NRT-code), using OOA 5-folding based on linear OA(3¹¹⁷, 4783000, F₃, 13) (dual of [4783000, 4782883, 14]-code), using

discarding factors / shortening the dual code based on linear OA(3¹¹⁷, 4783001, F₃, 13) (dual of [4783001, 4782884, 14]-code), using
- constructionÂ X applied to C_e(12) âŠ‚ C_e(9) [i] based on
  1. linear OA(3¹¹³, 4782969, F₃, 13) (dual of [4782969, 4782856, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 3¹⁴âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
  2. linear OA(3⁸⁵, 4782969, F₃, 10) (dual of [4782969, 4782884, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 3¹⁴âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
  3. linear OA(3⁴, 32, F₃, 2) (dual of [32, 28, 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(3¹¹⁷, 956600, F₃, 5, 12) (dual of [(956600, 5), 4782883, 13]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(3¹¹⁸, 956600, F₃, 5, 13) (dual of [(956600, 5), 4782882, 14]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(3¹¹⁹, 956600, F₃, 5, 13) (dual of [(956600, 5), 4782881, 14]-NRT-code)	[i]	OOA Duplication
4	Linear OOA(3¹⁷³, 1913200, F₃, 5, 13) (dual of [(1913200, 5), 9565827, 14]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs