MinT - Information on Result #984273

Information on Result #984273

Linear OOA(9²², 4375, F₉, 3, 6) (dual of [(4375, 3), 13103, 7]-NRT-code), using OOA 3-folding based on linear OA(9²², 13125, F₉, 6) (dual of [13125, 13103, 7]-code), using

discarding factors / shortening the dual code based on linear OA(9²², 13126, F₉, 6) (dual of [13126, 13104, 7]-code), using
- trace code [i] based on linear OA(81¹¹, 6563, F₈₁, 6) (dual of [6563, 6552, 7]-code), using
  - constructionÂ X applied to C_e(5) âŠ‚ C_e(4) [i] based on
    1. linear OA(81¹¹, 6561, F₈₁, 6) (dual of [6561, 6550, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 81²âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
    2. linear OA(81⁹, 6561, F₈₁, 5) (dual of [6561, 6552, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 81²âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
    3. linear OA(81⁰, 2, F₈₁, 0) (dual of [2, 2, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(81⁰, s, F₈₁, 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, 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		Method
1	Linear OOA(9²³, 4375, F₉, 3, 6) (dual of [(4375, 3), 13102, 7]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(9²⁵, 4385, F₉, 3, 6) (dual of [(4385, 3), 13130, 7]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
3	Linear OOA(9¹¹², 5596777, F₉, 3, 12) (dual of [(5596777, 3), 16790219, 13]-NRT-code)	[i]
4	Linear OOA(9¹²⁰, 5596777, F₉, 3, 13) (dual of [(5596777, 3), 16790211, 14]-NRT-code)	[i]