MinT - Information on Result #895005

Information on Result #895005

Linear OOA(3¹²¹, 4194418, F₃, 2, 11) (dual of [(4194418, 2), 8388715, 12]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3¹⁵, 117, F₃, 2, 5) (dual of [(117, 2), 219, 6]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. 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, 2, 5) (dual of [(77, 2), 143, 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, 4194301, F₃, 2, 11) (dual of [(4194301, 2), 8388496, 12]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3¹⁰⁶, 8388602, F₃, 11) (dual of [8388602, 8388496, 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(3¹²¹, 2097209, F₃, 4, 11) (dual of [(2097209, 4), 8388715, 12]-NRT-code)	[i]		OOA Folding