MinT - Information on Result #1604826

Information on Result #1604826

Linear OOA(3¹⁴⁵, 7679, F₃, 4, 24) (dual of [(7679, 4), 30571, 25]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁴⁵, 7679, F₃, 2, 24) (dual of [(7679, 2), 15213, 25]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁴⁵, 9846, F₃, 2, 24) (dual of [(9846, 2), 19547, 25]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3¹⁴⁵, 19692, F₃, 24) (dual of [19692, 19547, 25]-code), using
  - 1 times truncation [i] based on linear OA(3¹⁴⁶, 19693, F₃, 25) (dual of [19693, 19547, 26]-code), using
    - constructionÂ X applied to C_e(24) âŠ‚ C_e(22) [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(3¹³⁶, 19683, F₃, 23) (dual of [19683, 19547, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [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(3¹⁴⁵, 2559, F₃, 28, 24) (dual of [(2559, 28), 71507, 25]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row