MinT - Information on Result #2642962

Information on Result #2642962

Linear OOA(8⁴², 67, F₈, 3, 23) (dual of [(67, 3), 159, 24]-NRT-code), using strength reduction based on linear OOA(8⁴², 67, F₈, 3, 24) (dual of [(67, 3), 159, 25]-NRT-code), using

constructionÂ X applied to AG(3;F,167P) âŠ‚ AG(3;F,172P) [i] based on
1. linear OOA(8³⁸, 64, F₈, 3, 24) (dual of [(64, 3), 154, 25]-NRT-code), using algebraic-geometric NRT-code AG(3;F,167P) [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(8³³, 64, F₈, 3, 19) (dual of [(64, 3), 159, 20]-NRT-code), using algebraic-geometric NRT-code AG(3;F,172P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
3. linear OOA(8⁴, 3, F₈, 3, 4) (dual of [(3, 3), 5, 5]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(8⁴, 8, F₈, 3, 4) (dual of [(8, 3), 20, 5]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(3;20,8) [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	Digital (19, 42, 67)-net over F₈	[i]		Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound