MinT - Information on Result #2701158

Information on Result #2701158

Linear OOA(8¹⁶⁵, 371, F₈, 3, 61) (dual of [(371, 3), 948, 62]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(8¹⁶², 370, F₈, 3, 61) (dual of [(370, 3), 948, 62]-NRT-code), using

trace code [i] based on linear OOA(64⁸¹, 185, F₆₄, 3, 61) (dual of [(185, 3), 474, 62]-NRT-code), using
- constructionÂ X applied to AG(3;F,466P) âŠ‚ AG(3;F,480P) [i] based on
  1. linear OOA(64⁶⁸, 176, F₆₄, 3, 61) (dual of [(176, 3), 460, 62]-NRT-code), using algebraic-geometric NRT-code AG(3;F,466P) [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(64⁵⁴, 176, F₆₄, 3, 47) (dual of [(176, 3), 474, 48]-NRT-code), using algebraic-geometric NRT-code AG(3;F,480P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177 (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.