MinT - Information on Result #895504

Information on Result #895504

Linear OOA(4¹²⁶, 4194496, F₄, 2, 12) (dual of [(4194496, 2), 8388866, 13]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(4¹⁸, 195, F₄, 2, 6) (dual of [(195, 2), 372, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (12, 18, 195)-net over F₄, using
  - trace code for nets [i] based on digital (0, 6, 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(4¹⁰⁸, 4194301, F₄, 2, 12) (dual of [(4194301, 2), 8388494, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4¹⁰⁸, 8388602, F₄, 12) (dual of [8388602, 8388494, 13]-code), using
  - discarding factors / shortening the dual code based on linear OA(4¹⁰⁸, large, F₄, 12) (dual of [large, large−108, 13]-code), using
    - the primitive narrow-sense BCH-code C(I) with length 16777215Â = 4¹²âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(4¹²⁸, 4194497, F₄, 2, 12) (dual of [(4194497, 2), 8388866, 13]-NRT-code)	[i]		NRT-Code Embedding in Larger Space