MinT - Information on Result #1649583

Information on Result #1649583

Linear OOA(3²¹⁷, 132863, F₃, 5, 27) (dual of [(132863, 5), 664098, 28]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²¹⁷, 132863, F₃, 4, 27) (dual of [(132863, 4), 531235, 28]-NRT-code), using

OOA 4-folding [i] based on linear OA(3²¹⁷, 531452, F₃, 27) (dual of [531452, 531235, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(3²¹⁷, 531453, F₃, 27) (dual of [531453, 531236, 28]-code), using
  - 1 times truncation [i] based on linear OA(3²¹⁸, 531454, F₃, 28) (dual of [531454, 531236, 29]-code), using
    - constructionÂ X applied to C_e(27) âŠ‚ C_e(25) [i] based on
      1. 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]
      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(3¹, 13, F₃, 1) (dual of [13, 12, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(3¹, s, F₃, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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(3²¹⁷, 44287, F₃, 35, 27) (dual of [(44287, 35), 1549828, 28]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row