MinT - Information on Result #2646186

Information on Result #2646186

Linear OOA(8¹⁷¹, 100, F₈, 3, 129) (dual of [(100, 3), 129, 130]-NRT-code), using strength reduction based on linear OOA(8¹⁷¹, 100, F₈, 3, 130) (dual of [(100, 3), 129, 131]-NRT-code), using

constructionÂ X applied to AG(3;F,160P) âŠ‚ AG(3;F,165P) [i] based on
1. linear OOA(8¹⁶⁷, 97, F₈, 3, 130) (dual of [(97, 3), 124, 131]-NRT-code), using algebraic-geometric NRT-code AG(3;F,160P) [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 98, using
  - F₅ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]
2. linear OOA(8¹⁶², 97, F₈, 3, 125) (dual of [(97, 3), 129, 126]-NRT-code), using algebraic-geometric NRT-code AG(3;F,165P) [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 98 (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

None.