MinT - Information on Result #2645404

Information on Result #2645404

Linear OOA(8¹⁵¹, 69, F₈, 3, 129) (dual of [(69, 3), 56, 130]-NRT-code), using strength reduction based on linear OOA(8¹⁵¹, 69, F₈, 3, 130) (dual of [(69, 3), 56, 131]-NRT-code), using

constructionÂ X applied to AG(3;F,61P) âŠ‚ AG(3;F,69P) [i] based on
1. linear OOA(8¹⁴⁴, 64, F₈, 3, 130) (dual of [(64, 3), 48, 131]-NRT-code), using algebraic-geometric NRT-code AG(3;F,61P) [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(8¹³⁶, 64, F₈, 3, 122) (dual of [(64, 3), 56, 123]-NRT-code), using algebraic-geometric NRT-code AG(3;F,69P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
3. linear OOA(8⁷, 5, F₈, 3, 7) (dual of [(5, 3), 8, 8]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(8⁷, 8, F₈, 3, 7) (dual of [(8, 3), 17, 8]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(3;17,8) [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.