MinT - Information on Result #1022000

Information on Result #1022000

Linear OOA(8²², 333, F₈, 3, 7) (dual of [(333, 3), 977, 8]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(8³, 73, F₈, 3, 2) (dual of [(73, 3), 216, 3]-NRT-code), using
- appending 1 arbitrary column [i] based on linear OOA(8³, 73, F₈, 2, 2) (dual of [(73, 2), 143, 3]-NRT-code), using
  - appending kth column [i] based on linear OA(8³, 73, F₈, 2) (dual of [73, 70, 3]-code), using
    - Hamming code H(3,8) [i]
linear OOA(8⁵, 130, F₈, 3, 3) (dual of [(130, 3), 385, 4]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8⁵, 207, F₈, 3, 3) (dual of [(207, 3), 616, 4]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OA(8⁵, 208, F₈, 3) (dual of [208, 203, 4]-code or 208-cap in PG(4,8)), using
    - caps completed using a computer search [i]
linear OOA(8¹⁴, 130, F₈, 3, 7) (dual of [(130, 3), 376, 8]-NRT-code), using
- extracting embedded OOA [i] based on digital (7, 14, 130)-net over F₈, using
  - trace code for nets [i] based on digital (0, 7, 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]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(8¹³⁶, 5592735, F₈, 3, 15) (dual of [(5592735, 3), 16778069, 16]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(8¹²⁸, 5592735, F₈, 3, 14) (dual of [(5592735, 3), 16778077, 15]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
3	Linear OOA(8²², 332, F₈, 9, 7) (dual of [(332, 9), 2966, 8]-NRT-code)	[i]	OOA Stacking with Additional Row