MinT - Information on Result #1524214

Information on Result #1524214

Linear OOA(3¹⁴⁸, 8987, F₃, 3, 24) (dual of [(8987, 3), 26813, 25]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁴⁸, 8987, F₃, 2, 24) (dual of [(8987, 2), 17826, 25]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁴⁸, 9852, F₃, 2, 24) (dual of [(9852, 2), 19556, 25]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3¹⁴⁶, 9851, F₃, 2, 24) (dual of [(9851, 2), 19556, 25]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3¹⁴⁶, 19702, F₃, 24) (dual of [19702, 19556, 25]-code), using
    - constructionÂ X applied to C_e(24) âŠ‚ C_e(21) [i] based on
      1. linear OA(3¹⁴⁵, 19683, F₃, 25) (dual of [19683, 19538, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
      2. linear OA(3¹²⁷, 19683, F₃, 22) (dual of [19683, 19556, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
      3. linear OA(3¹, 19, F₃, 1) (dual of [19, 18, 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(3¹⁴⁸, 4493, F₃, 5, 24) (dual of [(4493, 5), 22317, 25]-NRT-code)	[i]		OOA Folding