MinT - Information on Result #2649303

Information on Result #2649303

Linear OOA(64⁸⁹, 521, F₆₄, 3, 47) (dual of [(521, 3), 1474, 48]-NRT-code), using strength reduction based on linear OOA(64⁸⁹, 521, F₆₄, 3, 48) (dual of [(521, 3), 1474, 49]-NRT-code), using

constructionÂ X applied to AG(3;F,1487P) âŠ‚ AG(3;F,1501P) [i] based on
1. linear OOA(64⁷⁶, 512, F₆₄, 3, 48) (dual of [(512, 3), 1460, 49]-NRT-code), using algebraic-geometric NRT-code AG(3;F,1487P) [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(64⁶², 512, F₆₄, 3, 34) (dual of [(512, 3), 1474, 35]-NRT-code), using algebraic-geometric NRT-code AG(3;F,1501P) [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513 (see above)
3. linear OOA(64¹³, 9, F₆₄, 3, 13) (dual of [(9, 3), 14, 14]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(64¹³, 64, F₆₄, 3, 13) (dual of [(64, 3), 179, 14]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(3;179,64) [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

None.