MinT - Information on Result #1117190

Information on Result #1117190

Linear OOA(3¹²¹, 1677837, F₃, 5, 11) (dual of [(1677837, 5), 8389064, 12]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3¹⁵, 117, F₃, 5, 5) (dual of [(117, 5), 570, 6]-NRT-code), using
- appending kth column [i] based on linear OOA(3¹⁵, 117, F₃, 4, 5) (dual of [(117, 4), 453, 6]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(3⁴, 40, F₃, 4, 2) (dual of [(40, 4), 156, 3]-NRT-code), using
      - appending 2 arbitrary columns [i] based on linear OOA(3⁴, 40, F₃, 2, 2) (dual of [(40, 2), 76, 3]-NRT-code), using
        appending kth column [i] based on linear OA(3⁴, 40, F₃, 2) (dual of [40, 36, 3]-code), using
        Hamming code H(4,3) [i]
    2. 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.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3¹⁸⁴, 5033511, F₃, 5, 11) (dual of [(5033511, 5), 25167371, 12]-NRT-code)	[i]		Generalized (u,Â u+v)-Construction for OOAs
2	Linear OOA(3¹²¹, 1677836, F₃, 15, 11) (dual of [(1677836, 15), 25167419, 12]-NRT-code)	[i]		OOA Stacking with Additional Row