MinT - Information on Result #973258

Information on Result #973258

Linear OOA(5¹²⁷, 5210, F₅, 3, 27) (dual of [(5210, 3), 15503, 28]-NRT-code), using OOA 3-folding based on linear OA(5¹²⁷, 15630, F₅, 27) (dual of [15630, 15503, 28]-code), using

discarding factors / shortening the dual code based on linear OA(5¹²⁷, 15631, F₅, 27) (dual of [15631, 15504, 28]-code), using
- constructionÂ X applied to C_e(26) âŠ‚ C_e(25) [i] based on
  1. linear OA(5¹²⁷, 15625, F₅, 27) (dual of [15625, 15498, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 5⁶âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
  2. linear OA(5¹²¹, 15625, F₅, 26) (dual of [15625, 15504, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 5⁶âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
  3. linear OA(5⁰, 6, F₅, 0) (dual of [6, 6, 1]-code), using
    - discarding factors / shortening the dual code based on linear OA(5⁰, s, F₅, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
      - OA with only one run / dual of code without redundancy [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(5¹²⁸, 5210, F₅, 3, 27) (dual of [(5210, 3), 15502, 28]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(5¹⁴³, 5226, F₅, 3, 27) (dual of [(5226, 3), 15535, 28]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
3	Linear OOA(5¹⁴⁴, 5228, F₅, 3, 27) (dual of [(5228, 3), 15540, 28]-NRT-code)	[i]
4	Linear OOA(5¹⁴⁵, 5230, F₅, 3, 27) (dual of [(5230, 3), 15545, 28]-NRT-code)	[i]
5	Linear OOA(5¹⁴⁶, 5231, F₅, 3, 27) (dual of [(5231, 3), 15547, 28]-NRT-code)	[i]
6	Linear OOA(5¹⁴⁷, 5232, F₅, 3, 27) (dual of [(5232, 3), 15549, 28]-NRT-code)	[i]