MinT - Information on Result #1008769

Information on Result #1008769

Linear OOA(3²⁴⁰, 3188650, F₃, 3, 20) (dual of [(3188650, 3), 9565710, 21]-NRT-code), using trace code based on linear OOA(9¹²⁰, 1594325, F₉, 3, 20) (dual of [(1594325, 3), 4782855, 21]-NRT-code), using

OOA 3-folding [i] based on linear OA(9¹²⁰, 4782975, F₉, 20) (dual of [4782975, 4782855, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(9¹²⁰, 4782976, F₉, 20) (dual of [4782976, 4782856, 21]-code), using
  - constructionÂ X applied to C_e(19) âŠ‚ C_e(18) [i] based on
    1. linear OA(9¹²⁰, 4782969, F₉, 20) (dual of [4782969, 4782849, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
    2. linear OA(9¹¹³, 4782969, F₉, 19) (dual of [4782969, 4782856, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
    3. linear OA(9⁰, 7, F₉, 0) (dual of [7, 7, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(9⁰, s, F₉, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Linear OOA(3²⁴³, 3188651, F₃, 3, 20) (dual of [(3188651, 3), 9565710, 21]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(3²⁴¹, 3188650, F₃, 3, 20) (dual of [(3188650, 3), 9565709, 21]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(3²⁴², 3188650, F₃, 3, 20) (dual of [(3188650, 3), 9565708, 21]-NRT-code)	[i]	OOA Duplication