MinT - Information on Result #1235325

Information on Result #1235325

Linear OOA(3²⁴², 4793518, F₃, 5, 15) (dual of [(4793518, 5), 23967348, 16]-NRT-code), using extracting embedded OOA based on digital (227, 242, 4793518)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (7, 14, 34)-net over F₃, using
  - linear code embedding found in a computer search [i]
2. digital (213, 228, 4793484)-net over F₃, using
  - trace code for nets [i] based on digital (42, 57, 1198371)-net over F₈₁, using
    - net defined by OOA [i] based on linear OOA(81⁵⁷, 1198371, F₈₁, 15, 15) (dual of [(1198371, 15), 17975508, 16]-NRT-code), using
      - OOA 7-folding and stacking with additional row [i] based on linear OA(81⁵⁷, 8388598, F₈₁, 15) (dual of [8388598, 8388541, 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		This result only	Method
1	Linear OOA(3²⁴³, 4793518, F₃, 5, 15) (dual of [(4793518, 5), 23967347, 16]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(3²⁴⁴, 4793518, F₃, 5, 15) (dual of [(4793518, 5), 23967346, 16]-NRT-code)	[i]		OOA Duplication