MinT - Information on Result #1605907

Information on Result #1605907

Linear OOA(3¹⁶³, 19722, F₃, 4, 24) (dual of [(19722, 4), 78725, 25]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁶³, 19722, F₃, 2, 24) (dual of [(19722, 2), 39281, 25]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁶³, 29535, F₃, 2, 24) (dual of [(29535, 2), 58907, 25]-NRT-code), using
- 3¹ times duplication [i] based on linear OOA(3¹⁶², 29535, F₃, 2, 24) (dual of [(29535, 2), 58908, 25]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3¹⁶², 59070, F₃, 24) (dual of [59070, 58908, 25]-code), using
    - constructionÂ X applied to C_e(24) âŠ‚ C_e(21) [i] based on
      1. linear OA(3¹⁶¹, 59049, F₃, 25) (dual of [59049, 58888, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
      2. linear OA(3¹⁴¹, 59049, F₃, 22) (dual of [59049, 58908, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
      3. linear OA(3¹, 21, F₃, 1) (dual of [21, 20, 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(3¹⁶³, 6573, F₃, 28, 24) (dual of [(6573, 28), 183881, 25]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row