MinT - Information on Result #1602861

Information on Result #1602861

Linear OOA(3¹⁰⁵, 9775, F₃, 4, 17) (dual of [(9775, 4), 38995, 18]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁰⁵, 9775, F₃, 2, 17) (dual of [(9775, 2), 19445, 18]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁰⁵, 9853, F₃, 2, 17) (dual of [(9853, 2), 19601, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3¹⁰⁵, 19706, F₃, 17) (dual of [19706, 19601, 18]-code), using
  - 1 times code embedding in larger space [i] based on linear OA(3¹⁰⁴, 19705, F₃, 17) (dual of [19705, 19601, 18]-code), using
    - constructionÂ X applied to C_e(16) âŠ‚ C_e(13) [i] based on
      1. linear OA(3¹⁰⁰, 19683, F₃, 17) (dual of [19683, 19583, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
      2. linear OA(3⁸², 19683, F₃, 14) (dual of [19683, 19601, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [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(3¹⁰⁵, 4887, F₃, 20, 17) (dual of [(4887, 20), 97635, 18]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row