MinT - Information on Result #1117768

Information on Result #1117768

Linear OOA(3²¹⁶, 1678048, F₃, 5, 18) (dual of [(1678048, 5), 8390024, 19]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3³⁶, 328, F₃, 5, 9) (dual of [(328, 5), 1604, 10]-NRT-code), using
- extracting embedded OOA [i] based on digital (27, 36, 328)-net over F₃, using
  - trace code for nets [i] based on digital (0, 9, 82)-net over F₈₁, using
    - net from sequence [i] based on digital (0, 81)-sequence over F₈₁, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 0 and N(F) ≥ 82, using
        the rational function field F₈₁(x) [i]
      - Niederreiter sequence [i]
linear OOA(3¹⁸⁰, 1677720, F₃, 5, 18) (dual of [(1677720, 5), 8388420, 19]-NRT-code), using
- OOA 5-folding [i] based on linear OA(3¹⁸⁰, 8388600, F₃, 18) (dual of [8388600, 8388420, 19]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁸⁰, large, F₃, 18) (dual of [large, large−180, 19]-code), using
    - the primitive narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3²¹⁸, 1678048, F₃, 5, 18) (dual of [(1678048, 5), 8390022, 19]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(3²¹⁹, 1678048, F₃, 5, 18) (dual of [(1678048, 5), 8390021, 19]-NRT-code)	[i]		OOA Duplication