MinT - Information on Result #1117098

Information on Result #1117098

Linear OOA(3¹⁰⁹, 1678005, F₃, 5, 10) (dual of [(1678005, 5), 8389916, 11]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3¹⁸, 285, F₃, 5, 5) (dual of [(285, 5), 1407, 6]-NRT-code), using
- appending kth column [i] based on linear OOA(3¹⁸, 285, F₃, 4, 5) (dual of [(285, 4), 1122, 6]-NRT-code), using
  - generalized (u,Â u+v)-construction [i] based on
    1. linear OOA(3¹, 95, F₃, 4, 1) (dual of [(95, 4), 379, 2]-NRT-code), using
      - discarding factors / shortening the dual code based on linear OOA(3¹, s, F₃, 4, 1) for arbitrarily large s, using
        appending 3 arbitrary columns [i] based on linear OA(3¹, s, F₃, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
    2. linear OOA(3⁵, 95, F₃, 4, 2) (dual of [(95, 4), 375, 3]-NRT-code), using
      - discarding factors / shortening the dual code based on linear OOA(3⁵, 121, F₃, 4, 2) (dual of [(121, 4), 479, 3]-NRT-code), using
        appending 2 arbitrary columns [i] based on linear OOA(3⁵, 121, F₃, 2, 2) (dual of [(121, 2), 237, 3]-NRT-code), using
        appending kth column [i] based on linear OA(3⁵, 121, F₃, 2) (dual of [121, 116, 3]-code), using
        Hamming code H(5,3) [i]
    3. linear OOA(3¹², 95, F₃, 4, 5) (dual of [(95, 4), 368, 6]-NRT-code), using
      - extracting embedded OOA [i] based on digital (7, 12, 95)-net over F₃, using
        linear code embedding found in a computer search [i]
linear OOA(3⁹¹, 1677720, F₃, 5, 10) (dual of [(1677720, 5), 8388509, 11]-NRT-code), using
- OOA 5-folding [i] based on linear OA(3⁹¹, 8388600, F₃, 10) (dual of [8388600, 8388509, 11]-code), using
  - discarding factors / shortening the dual code based on linear OA(3⁹¹, large, F₃, 10) (dual of [large, large−91, 11]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [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(3¹⁷², 5034015, F₃, 5, 10) (dual of [(5034015, 5), 25169903, 11]-NRT-code)	[i]		Generalized (u,Â u+v)-Construction for OOAs
2	Linear OOA(3¹⁰⁹, 1678004, F₃, 15, 10) (dual of [(1678004, 15), 25169951, 11]-NRT-code)	[i]		OOA Stacking with Additional Row