MinT - Information on Result #1107237

Information on Result #1107237

Linear OOA(3³⁹, 265730, F₃, 5, 5) (dual of [(265730, 5), 1328611, 6]-NRT-code), using appending kth column based on linear OOA(3³⁹, 265730, F₃, 4, 5) (dual of [(265730, 4), 1062881, 6]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(3², 4, F₃, 4, 2) (dual of [(4, 4), 14, 3]-NRT-code), using
  - extended Reedâ€“Solomon NRT-code RS_e(4;14,3) [i]
2. linear OOA(3³⁷, 265726, F₃, 4, 5) (dual of [(265726, 4), 1062867, 6]-NRT-code), using
  - OOA 2-folding and stacking with additional row [i] based on linear OA(3³⁷, 531453, F₃, 5) (dual of [531453, 531416, 6]-code), using
    - constructionÂ X applied to C_e(4) âŠ‚ C_e(3) [i] based on
      1. linear OA(3³⁷, 531441, F₃, 5) (dual of [531441, 531404, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
      2. linear OA(3²⁵, 531441, F₃, 4) (dual of [531441, 531416, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [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: 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(3¹⁴⁵, 1943450, F₃, 5, 11) (dual of [(1943450, 5), 9717105, 12]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Digital (34, 39, 265730)-net over F₃	[i]		Net Defined by OOA