MinT - Information on Result #2510437

Information on Result #2510437

Linear OOA(8¹⁵², 420, F₈, 2, 49) (dual of [(420, 2), 688, 50]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(8¹⁵⁰, 419, F₈, 2, 49) (dual of [(419, 2), 688, 50]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(8³⁸, 65, F₈, 2, 24) (dual of [(65, 2), 92, 25]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,105P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
    - the Suzuki function field over F₈ [i]
2. linear OOA(8¹¹², 354, F₈, 2, 49) (dual of [(354, 2), 596, 50]-NRT-code), using
  - extracting embedded OOA [i] based on digital (63, 112, 354)-net over F₈, using
    - trace code for nets [i] based on digital (7, 56, 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(8¹⁵², 210, F₈, 3, 49) (dual of [(210, 3), 478, 50]-NRT-code)	[i]		OOA Folding