MinT - Information on Result #2649043

Information on Result #2649043

Linear OOA(64⁷⁷, 515, F₆₄, 3, 44) (dual of [(515, 3), 1468, 45]-NRT-code), using strength reduction based on linear OOA(64⁷⁷, 515, F₆₄, 3, 45) (dual of [(515, 3), 1468, 46]-NRT-code), using

constructionÂ X applied to AG(3;F,1490P) âŠ‚ AG(3;F,1495P) [i] based on
1. linear OOA(64⁷³, 512, F₆₄, 3, 45) (dual of [(512, 3), 1463, 46]-NRT-code), using algebraic-geometric NRT-code AG(3;F,1490P) [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
  - the Hermitian function field over F₆₄ [i]
2. linear OOA(64⁶⁸, 512, F₆₄, 3, 40) (dual of [(512, 3), 1468, 41]-NRT-code), using algebraic-geometric NRT-code AG(3;F,1495P) [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513 (see above)
3. linear OOA(64⁴, 3, F₆₄, 3, 4) (dual of [(3, 3), 5, 5]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(64⁴, 64, F₆₄, 3, 4) (dual of [(64, 3), 188, 5]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(3;188,64) [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 (33, 77, 515)-net over F₆₄	[i]		Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound