MinT - Information on Result #895692

Information on Result #895692

Linear OOA(4²¹⁴, 4194541, F₄, 2, 21) (dual of [(4194541, 2), 8388868, 22]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(4³³, 240, F₄, 2, 10) (dual of [(240, 2), 447, 11]-NRT-code), using
- extracting embedded OOA [i] based on digital (23, 33, 240)-net over F₄, using
  - trace code for nets [i] based on digital (1, 11, 80)-net over F₆₄, using
    - net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
        a function field by SÃ©mirat [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(4²¹⁴, 4194541, F₄, 2, 20) (dual of [(4194541, 2), 8388868, 21]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(4²¹⁶, 4194542, F₄, 2, 21) (dual of [(4194542, 2), 8388868, 22]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
3	Linear OOA(4²¹⁵, 4194541, F₄, 2, 21) (dual of [(4194541, 2), 8388867, 22]-NRT-code)	[i]	OOA Duplication
4	Linear OOA(4²¹⁴, 838908, F₄, 22, 21) (dual of [(838908, 22), 18455762, 22]-NRT-code)	[i]	OOA Folding and Stacking with Additional Row