MinT - Information on Result #1523817

Information on Result #1523817

Linear OOA(3¹⁴¹, 8576, F₃, 3, 23) (dual of [(8576, 3), 25587, 24]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁴¹, 8576, F₃, 2, 23) (dual of [(8576, 2), 17011, 24]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁴¹, 9853, F₃, 2, 23) (dual of [(9853, 2), 19565, 24]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3¹⁴¹, 19706, F₃, 23) (dual of [19706, 19565, 24]-code), using
  - 1 times code embedding in larger space [i] based on linear OA(3¹⁴⁰, 19705, F₃, 23) (dual of [19705, 19565, 24]-code), using
    - constructionÂ X applied to C_e(22) âŠ‚ C_e(19) [i] based on
      1. 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]
      2. linear OA(3¹¹⁸, 19683, F₃, 20) (dual of [19683, 19565, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
      3. linear OA(3⁴, 22, F₃, 2) (dual of [22, 18, 3]-code), using
        discarding factors / shortening the dual code based on linear OA(3⁴, 40, F₃, 2) (dual of [40, 36, 3]-code), using
        Hamming code H(4,3) [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(3¹⁴¹, 4288, F₃, 5, 23) (dual of [(4288, 5), 21299, 24]-NRT-code)	[i]		OOA Folding