MinT - Information on Result #896937

Information on Result #896937

Linear OOA(8¹²⁶, 514, F₈, 2, 37) (dual of [(514, 2), 902, 38]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8³⁸, 160, F₈, 2, 18) (dual of [(160, 2), 282, 19]-NRT-code), using
- extracting embedded OOA [i] based on digital (20, 38, 160)-net over F₈, using
  - trace code for nets [i] based on digital (1, 19, 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(8⁸⁸, 354, F₈, 2, 37) (dual of [(354, 2), 620, 38]-NRT-code), using
- extracting embedded OOA [i] based on digital (51, 88, 354)-net over F₈, using
  - trace code for nets [i] based on digital (7, 44, 177)-net over F₆₄, using
    - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
        a function field by GarcÃa and Quoos [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(8¹²⁸, 515, F₈, 2, 37) (dual of [(515, 2), 902, 38]-NRT-code)	[i]		NRT-Code Embedding in Larger Space
2	Linear OOA(8¹²⁷, 514, F₈, 2, 37) (dual of [(514, 2), 901, 38]-NRT-code)	[i]		OOA Duplication