MinT - Information on Result #895688

Information on Result #895688

Linear OOA(4²⁰⁷, 4194377, F₄, 2, 21) (dual of [(4194377, 2), 8388547, 22]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(4²⁶, 76, F₄, 2, 10) (dual of [(76, 2), 126, 11]-NRT-code), using
- extracting embedded OOA [i] based on digital (16, 26, 76)-net over F₄, using
  - trace code for nets [i] based on digital (3, 13, 38)-net over F₁₆, using
    - net from sequence [i] based on digital (3, 37)-sequence over F₁₆, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 3 and N(F) ≥ 38, 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(4²⁰⁷, 4194377, F₄, 2, 20) (dual of [(4194377, 2), 8388547, 21]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(4²⁰⁸, 4194377, F₄, 2, 21) (dual of [(4194377, 2), 8388546, 22]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(4²⁰⁷, 838875, F₄, 22, 21) (dual of [(838875, 22), 18455043, 22]-NRT-code)	[i]	OOA Folding and Stacking with Additional Row