MinT - Information on Result #1117192

Information on Result #1117192

Linear OOA(3¹²³, 1677951, F₃, 5, 11) (dual of [(1677951, 5), 8389632, 12]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3¹⁷, 231, F₃, 5, 5) (dual of [(231, 5), 1138, 6]-NRT-code), using
- appending kth column [i] based on linear OOA(3¹⁷, 231, F₃, 4, 5) (dual of [(231, 4), 907, 6]-NRT-code), using
  - generalized (u,Â u+v)-construction [i] based on
    1. linear OOA(3¹, 77, F₃, 4, 1) (dual of [(77, 4), 307, 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, 77, F₃, 4, 2) (dual of [(77, 4), 303, 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(3¹¹, 77, F₃, 4, 5) (dual of [(77, 4), 297, 6]-NRT-code), using
      - extracting embedded OOA [i] based on digital (6, 11, 77)-net over F₃, using
        linear code embedding found in a computer search [i]
linear OOA(3¹⁰⁶, 1677720, F₃, 5, 11) (dual of [(1677720, 5), 8388494, 12]-NRT-code), using
- OOA 5-folding [i] based on linear OA(3¹⁰⁶, 8388600, F₃, 11) (dual of [8388600, 8388494, 12]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁰⁶, large, F₃, 11) (dual of [large, large−106, 12]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [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(3¹⁸⁶, 5033853, F₃, 5, 11) (dual of [(5033853, 5), 25169079, 12]-NRT-code)	[i]		Generalized (u,Â u+v)-Construction for OOAs
2	Linear OOA(3¹²³, 1677950, F₃, 15, 11) (dual of [(1677950, 15), 25169127, 12]-NRT-code)	[i]		OOA Stacking with Additional Row