MinT - Information on Result #894995

Information on Result #894995

Linear OOA(3¹²⁹, 4783085, F₃, 2, 10) (dual of [(4783085, 2), 9566041, 11]-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(3¹¹⁴, 4782968, F₃, 2, 10) (dual of [(4782968, 2), 9565822, 11]-NRT-code), using
- trace code [i] based on linear OOA(9⁵⁷, 2391484, F₉, 2, 10) (dual of [(2391484, 2), 4782911, 11]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(9⁵⁷, 4782968, F₉, 10) (dual of [4782968, 4782911, 11]-code), using
    - discarding factors / shortening the dual code based on linear OA(9⁵⁷, 4782969, F₉, 10) (dual of [4782969, 4782912, 11]-code), using
      - an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3¹²⁹, 2391542, F₃, 4, 10) (dual of [(2391542, 4), 9566039, 11]-NRT-code)	[i]		OOA Folding