MinT - Information on Result #1650663

Information on Result #1650663

Linear OOA(3²²⁹, 132863, F₃, 5, 29) (dual of [(132863, 5), 664086, 30]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²²⁹, 132863, F₃, 4, 29) (dual of [(132863, 4), 531223, 30]-NRT-code), using

OOA 4-folding [i] based on linear OA(3²²⁹, 531452, F₃, 29) (dual of [531452, 531223, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(3²²⁹, 531453, F₃, 29) (dual of [531453, 531224, 30]-code), using
  - constructionÂ X applied to C_e(28) âŠ‚ C_e(27) [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(3²¹⁷, 531441, F₃, 28) (dual of [531441, 531224, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
    3. linear OA(3⁰, 12, F₃, 0) (dual of [12, 12, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(3⁰, s, F₃, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [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(3²³⁰, 132863, F₃, 5, 29) (dual of [(132863, 5), 664085, 30]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(3²³¹, 132863, F₃, 5, 29) (dual of [(132863, 5), 664084, 30]-NRT-code)	[i]		OOA Duplication
3	Linear OOA(3²²⁹, 44287, F₃, 35, 29) (dual of [(44287, 35), 1549816, 30]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row