MinT - Information on Result #1646178

Information on Result #1646178

Linear OOA(3¹⁷⁴, 7536, F₃, 5, 29) (dual of [(7536, 5), 37506, 30]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁷⁴, 7536, F₃, 2, 29) (dual of [(7536, 2), 14898, 30]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁷⁴, 9847, F₃, 2, 29) (dual of [(9847, 2), 19520, 30]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3¹⁷², 9846, F₃, 2, 29) (dual of [(9846, 2), 19520, 30]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3¹⁷², 19692, F₃, 29) (dual of [19692, 19520, 30]-code), using
    - constructionÂ X applied to C_e(28) âŠ‚ C_e(27) [i] based on
      1. linear OA(3¹⁷², 19683, F₃, 29) (dual of [19683, 19511, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
      2. linear OA(3¹⁶³, 19683, F₃, 28) (dual of [19683, 19520, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [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(3¹⁷⁴, 2511, F₃, 35, 29) (dual of [(2511, 35), 87711, 30]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row