MinT - Information on Result #1101095

Information on Result #1101095

Linear OOA(3²²⁸, 4194301, F₃, 5, 15) (dual of [(4194301, 5), 20971277, 16]-NRT-code), using OOA 2-folding based on linear OOA(3²²⁸, 8388602, F₃, 3, 15) (dual of [(8388602, 3), 25165578, 16]-NRT-code), using

trace code [i] based on linear OOA(9¹¹⁴, 4194301, F₉, 3, 15) (dual of [(4194301, 3), 12582789, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(9¹¹⁴, 8388602, F₉, 2, 15) (dual of [(8388602, 2), 16777090, 16]-NRT-code), using
  - trace code [i] based on linear OOA(81⁵⁷, 4194301, F₈₁, 2, 15) (dual of [(4194301, 2), 8388545, 16]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(81⁵⁷, 8388602, F₈₁, 15) (dual of [8388602, 8388545, 16]-code), using
      - discarding factors / shortening the dual code based on linear OA(81⁵⁷, large, F₈₁, 15) (dual of [large, large−57, 16]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 21523361Â | 81⁸âˆ’1, defining interval IÂ =Â [0,7], and minimum distance dÂ â‰¥ |{−7,−6,…,7}|+1Â =Â 16 (BCH-bound) [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(3²³⁵, 4194305, F₃, 5, 15) (dual of [(4194305, 5), 20971290, 16]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(3²³⁶, 4194308, F₃, 5, 15) (dual of [(4194308, 5), 20971304, 16]-NRT-code)	[i]
3	Linear OOA(3²³⁷, 4194310, F₃, 5, 15) (dual of [(4194310, 5), 20971313, 16]-NRT-code)	[i]
4	Linear OOA(3²³⁸, 4194312, F₃, 5, 15) (dual of [(4194312, 5), 20971322, 16]-NRT-code)	[i]
5	Linear OOA(3²³⁹, 4194316, F₃, 5, 15) (dual of [(4194316, 5), 20971341, 16]-NRT-code)	[i]
6	Linear OOA(3²⁴⁰, 4194321, F₃, 5, 15) (dual of [(4194321, 5), 20971365, 16]-NRT-code)	[i]
7	Linear OOA(3²⁴¹, 4194327, F₃, 5, 15) (dual of [(4194327, 5), 20971394, 16]-NRT-code)	[i]
8	Linear OOA(3²⁴², 4194335, F₃, 5, 15) (dual of [(4194335, 5), 20971433, 16]-NRT-code)	[i]
9	Linear OOA(3²⁴⁵, 4194341, F₃, 5, 15) (dual of [(4194341, 5), 20971460, 16]-NRT-code)	[i]
10	Linear OOA(3²⁴⁶, 4194347, F₃, 5, 15) (dual of [(4194347, 5), 20971489, 16]-NRT-code)	[i]
11	Linear OOA(3²⁴⁷, 4194355, F₃, 5, 15) (dual of [(4194355, 5), 20971528, 16]-NRT-code)	[i]
12	Linear OOA(3²⁴⁸, 4194369, F₃, 5, 15) (dual of [(4194369, 5), 20971597, 16]-NRT-code)	[i]
13	Linear OOA(3²⁴⁹, 4194385, F₃, 5, 15) (dual of [(4194385, 5), 20971676, 16]-NRT-code)	[i]