MinT - Information on Result #1646814

Information on Result #1646814

Linear OOA(3¹⁸³, 6831, F₃, 5, 31) (dual of [(6831, 5), 33972, 32]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁸³, 6831, F₃, 2, 31) (dual of [(6831, 2), 13479, 32]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁸³, 9847, F₃, 2, 31) (dual of [(9847, 2), 19511, 32]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3¹⁸³, 19694, F₃, 31) (dual of [19694, 19511, 32]-code), using
  - 1 times code embedding in larger space [i] based on linear OA(3¹⁸², 19693, F₃, 31) (dual of [19693, 19511, 32]-code), using
    - constructionÂ X applied to C_e(30) âŠ‚ C_e(28) [i] based on
      1. linear OA(3¹⁸¹, 19683, F₃, 31) (dual of [19683, 19502, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
      2. 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]
      3. linear OA(3¹, 10, F₃, 1) (dual of [10, 9, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(3¹, s, F₃, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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(3¹⁸³, 2276, F₃, 35, 31) (dual of [(2276, 35), 79477, 32]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row