MinT - Information on Result #941085

Information on Result #941085

Linear OOA(8¹³⁴, 422, F₈, 2, 41) (dual of [(422, 2), 710, 42]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8³⁸, 68, F₈, 2, 20) (dual of [(68, 2), 98, 21]-NRT-code), using
- constructionÂ X applied to AG(2;F,107P) âŠ‚ AG(2;F,112P) [i] based on
  1. linear OOA(8³⁴, 64, F₈, 2, 20) (dual of [(64, 2), 94, 21]-NRT-code), using algebraic-geometric NRT-code AG(2;F,107P) [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(8²⁹, 64, F₈, 2, 15) (dual of [(64, 2), 99, 16]-NRT-code), using algebraic-geometric NRT-code AG(2;F,112P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
  3. linear OOA(8⁴, 4, F₈, 2, 4) (dual of [(4, 2), 4, 5]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(8⁴, 8, F₈, 2, 4) (dual of [(8, 2), 12, 5]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;12,8) [i]
linear OOA(8⁹⁶, 354, F₈, 2, 41) (dual of [(354, 2), 612, 42]-NRT-code), using
- extracting embedded OOA [i] based on digital (55, 96, 354)-net over F₈, using
  - trace code for nets [i] based on digital (7, 48, 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(8¹³⁴, 211, F₈, 3, 41) (dual of [(211, 3), 499, 42]-NRT-code)	[i]		OOA Folding