MinT - Information on Result #906195

Information on Result #906195

Linear OOA(3¹²², 4194458, F₃, 2, 11) (dual of [(4194458, 2), 8388794, 12]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3¹⁶, 157, F₃, 2, 5) (dual of [(157, 2), 298, 6]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(3¹, 40, F₃, 2, 1) (dual of [(40, 2), 79, 2]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(3¹, s, F₃, 2, 1) for arbitrarily large s, using
      - appending 1 arbitrary column [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(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]
  3. 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(3¹²², 2097229, F₃, 4, 11) (dual of [(2097229, 4), 8388794, 12]-NRT-code)	[i]		OOA Folding