MinT - Information on Result #1529090

Information on Result #1529090

Linear OOA(3²¹⁰, 8044, F₃, 3, 35) (dual of [(8044, 3), 23922, 36]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²¹⁰, 8044, F₃, 2, 35) (dual of [(8044, 2), 15878, 36]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3²¹⁰, 9847, F₃, 2, 35) (dual of [(9847, 2), 19484, 36]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3²⁰⁸, 9846, F₃, 2, 35) (dual of [(9846, 2), 19484, 36]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3²⁰⁸, 19692, F₃, 35) (dual of [19692, 19484, 36]-code), using
    - constructionÂ X applied to C_e(34) âŠ‚ C_e(33) [i] based on
      1. linear OA(3²⁰⁸, 19683, F₃, 35) (dual of [19683, 19475, 36]-code), using an extension C_e(34) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,34], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 35 [i]
      2. linear OA(3¹⁹⁹, 19683, F₃, 34) (dual of [19683, 19484, 35]-code), using an extension C_e(33) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,33], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 34 [i]
      3. linear OA(3⁰, 9, F₃, 0) (dual of [9, 9, 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(3²¹⁰, 4022, F₃, 5, 35) (dual of [(4022, 5), 19900, 36]-NRT-code)	[i]		OOA Folding