MinT - Information on Result #2701190

Information on Result #2701190

Linear OOA(8¹⁷¹, 374, F₈, 3, 62) (dual of [(374, 3), 951, 63]-NRT-code), using 8¹ times duplication based on linear OOA(8¹⁷⁰, 374, F₈, 3, 62) (dual of [(374, 3), 952, 63]-NRT-code), using

trace code [i] based on linear OOA(64⁸⁵, 187, F₆₄, 3, 62) (dual of [(187, 3), 476, 63]-NRT-code), using
- constructionÂ X applied to AG(3;F,465P) âŠ‚ AG(3;F,482P) [i] based on
  1. linear OOA(64⁶⁹, 176, F₆₄, 3, 62) (dual of [(176, 3), 459, 63]-NRT-code), using algebraic-geometric NRT-code AG(3;F,465P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
    - a function field by GarcÃa and Quoos [i]
  2. linear OOA(64⁵², 176, F₆₄, 3, 45) (dual of [(176, 3), 476, 46]-NRT-code), using algebraic-geometric NRT-code AG(3;F,482P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177 (see above)
  3. linear OOA(64¹⁶, 11, F₆₄, 3, 16) (dual of [(11, 3), 17, 17]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(64¹⁶, 64, F₆₄, 3, 16) (dual of [(64, 3), 176, 17]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(3;176,64) [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.