MinT - Information on Result #895691

Information on Result #895691

Linear OOA(4²¹¹, 4194496, F₄, 2, 21) (dual of [(4194496, 2), 8388781, 22]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(4³⁰, 195, F₄, 2, 10) (dual of [(195, 2), 360, 11]-NRT-code), using
- extracting embedded OOA [i] based on digital (20, 30, 195)-net over F₄, using
  - trace code for nets [i] based on digital (0, 10, 65)-net over F₆₄, using
    - net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
        the rational function field F₆₄(x) [i]
      - Niederreiter sequence [i]
linear OOA(4¹⁸¹, 4194301, F₄, 2, 21) (dual of [(4194301, 2), 8388421, 22]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4¹⁸¹, 8388602, F₄, 21) (dual of [8388602, 8388421, 22]-code), using
  - discarding factors / shortening the dual code based on linear OA(4¹⁸¹, large, F₄, 21) (dual of [large, large−181, 22]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 4¹²âˆ’1, defining interval IÂ =Â [0,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(4²¹¹, 4194496, F₄, 2, 20) (dual of [(4194496, 2), 8388781, 21]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(4²¹³, 4194497, F₄, 2, 21) (dual of [(4194497, 2), 8388781, 22]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
3	Linear OOA(4²¹², 4194496, F₄, 2, 21) (dual of [(4194496, 2), 8388780, 22]-NRT-code)	[i]	OOA Duplication
4	Linear OOA(4²¹¹, 838899, F₄, 22, 21) (dual of [(838899, 22), 18455567, 22]-NRT-code)	[i]	OOA Folding and Stacking with Additional Row