MinT - Information on Result #1094559

Information on Result #1094559

Linear OOA(3³⁶, 88582, F₃, 5, 5) (dual of [(88582, 5), 442874, 6]-NRT-code), using OOA stacking with additional row based on linear OOA(3³⁶, 88583, F₃, 2, 5) (dual of [(88583, 2), 177130, 6]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(3², 4, F₃, 2, 2) (dual of [(4, 2), 6, 3]-NRT-code), using
  - extended Reedâ€“Solomon NRT-code RS_e(2;6,3) [i]
2. linear OOA(3³⁴, 88579, F₃, 2, 5) (dual of [(88579, 2), 177124, 6]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3³⁴, 177158, F₃, 5) (dual of [177158, 177124, 6]-code), using
    - constructionÂ X applied to C_e(4) âŠ‚ C_e(3) [i] based on
      1. linear OA(3³⁴, 177147, F₃, 5) (dual of [177147, 177113, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
      2. linear OA(3²³, 177147, F₃, 4) (dual of [177147, 177124, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
      3. linear OA(3⁰, 11, F₃, 0) (dual of [11, 11, 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: 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		This result only	Method
1	Linear OOA(3¹²⁷, 1766302, F₃, 5, 10) (dual of [(1766302, 5), 8831383, 11]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Digital (31, 36, 88582)-net over F₃	[i]		Net Defined by OOA