MinT - Information on Result #1107236

Information on Result #1107236

Linear OOA(3³³, 29533, F₃, 5, 5) (dual of [(29533, 5), 147632, 6]-NRT-code), using appending kth column based on linear OOA(3³³, 29533, F₃, 4, 5) (dual of [(29533, 4), 118099, 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(3³¹, 29529, F₃, 4, 5) (dual of [(29529, 4), 118085, 6]-NRT-code), using
  - OOA 2-folding and stacking with additional row [i] based on linear OA(3³¹, 59059, F₃, 5) (dual of [59059, 59028, 6]-code), using
    - constructionÂ X applied to C_e(4) âŠ‚ C_e(3) [i] based on
      1. linear OA(3³¹, 59049, F₃, 5) (dual of [59049, 59018, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
      2. linear OA(3²¹, 59049, F₃, 4) (dual of [59049, 59028, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
      3. linear OA(3⁰, 10, F₃, 0) (dual of [10, 10, 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(3¹²⁴, 1707253, F₃, 5, 10) (dual of [(1707253, 5), 8536141, 11]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Digital (28, 33, 29533)-net over F₃	[i]		Net Defined by OOA