MinT - Information on Result #2510618

Information on Result #2510618

Linear OOA(8¹⁶⁹, 1030, F₈, 2, 53) (dual of [(1030, 2), 1891, 54]-NRT-code), using 8¹ times duplication based on linear OOA(8¹⁶⁸, 1030, F₈, 2, 53) (dual of [(1030, 2), 1892, 54]-NRT-code), using

trace code [i] based on linear OOA(64⁸⁴, 515, F₆₄, 2, 53) (dual of [(515, 2), 946, 54]-NRT-code), using
- constructionÂ X applied to AG(2;F,970P) âŠ‚ AG(2;F,974P) [i] based on
  1. linear OOA(64⁸¹, 512, F₆₄, 2, 53) (dual of [(512, 2), 943, 54]-NRT-code), using algebraic-geometric NRT-code AG(2;F,970P) [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(64⁷⁷, 512, F₆₄, 2, 49) (dual of [(512, 2), 947, 50]-NRT-code), using algebraic-geometric NRT-code AG(2;F,974P) [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513 (see above)
  3. linear OOA(64³, 3, F₆₄, 2, 3) (dual of [(3, 2), 3, 4]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(64³, 64, F₆₄, 2, 3) (dual of [(64, 2), 125, 4]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;125,64) [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.