MinT - Information on Result #1235257

Information on Result #1235257

Linear OOA(3²⁰⁹, 5592442, F₃, 5, 13) (dual of [(5592442, 5), 27962001, 14]-NRT-code), using extracting embedded OOA based on digital (196, 209, 5592442)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (7, 13, 42)-net over F₃, using
  - linear code embedding found in a computer search [i]
2. digital (183, 196, 5592400)-net over F₃, using
  - trace code for nets [i] based on digital (85, 98, 2796200)-net over F₉, using
    - net defined by OOA [i] based on linear OOA(9⁹⁸, 2796200, F₉, 14, 13) (dual of [(2796200, 14), 39146702, 14]-NRT-code), using
      - OOA 3-folding and stacking with additional row [i] based on linear OOA(9⁹⁸, 8388601, F₉, 2, 13) (dual of [(8388601, 2), 16777104, 14]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(9⁹⁸, 8388602, F₉, 2, 13) (dual of [(8388602, 2), 16777106, 14]-NRT-code), using
        trace code [i] based on linear OOA(81⁴⁹, 4194301, F₈₁, 2, 13) (dual of [(4194301, 2), 8388553, 14]-NRT-code), using
        OOA 2-folding [i] based on linear OA(81⁴⁹, 8388602, F₈₁, 13) (dual of [8388602, 8388553, 14]-code), using
        discarding factors / shortening the dual code based on linear OA(81⁴⁹, large, F₈₁, 13) (dual of [large, large−49, 14]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 21523361Â | 81⁸âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (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(3²¹⁰, 5592442, F₃, 5, 13) (dual of [(5592442, 5), 27962000, 14]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(3²¹¹, 5592442, F₃, 5, 13) (dual of [(5592442, 5), 27961999, 14]-NRT-code)	[i]		OOA Duplication