MinT - Information on Result #1651027

Information on Result #1651027

Linear OOA(3²³³, 132867, F₃, 5, 29) (dual of [(132867, 5), 664102, 30]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²³³, 132867, F₃, 4, 29) (dual of [(132867, 4), 531235, 30]-NRT-code), using

OOA 4-folding [i] based on linear OA(3²³³, 531468, F₃, 29) (dual of [531468, 531235, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(3²³³, 531469, F₃, 29) (dual of [531469, 531236, 30]-code), using
  - constructionÂ X applied to C_e(28) âŠ‚ C_e(25) [i] based on
    1. linear OA(3²²⁹, 531441, F₃, 29) (dual of [531441, 531212, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
    2. linear OA(3²⁰⁵, 531441, F₃, 26) (dual of [531441, 531236, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [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: 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		This result only	Method
1	Linear OOA(3²³⁴, 132867, F₃, 5, 29) (dual of [(132867, 5), 664101, 30]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(3²³³, 44288, F₃, 35, 29) (dual of [(44288, 35), 1549847, 30]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row