MinT - Information on Result #2510359

Information on Result #2510359

Linear OOA(8¹⁶³, 1036, F₈, 2, 47) (dual of [(1036, 2), 1909, 48]-NRT-code), using 8¹ times duplication based on linear OOA(8¹⁶², 1036, F₈, 2, 47) (dual of [(1036, 2), 1910, 48]-NRT-code), using

trace code [i] based on linear OOA(64⁸¹, 518, F₆₄, 2, 47) (dual of [(518, 2), 955, 48]-NRT-code), using
- constructionÂ X applied to AG(2;F,976P) âŠ‚ AG(2;F,983P) [i] based on
  1. linear OOA(64⁷⁵, 512, F₆₄, 2, 47) (dual of [(512, 2), 949, 48]-NRT-code), using algebraic-geometric NRT-code AG(2;F,976P) [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(64⁶⁸, 512, F₆₄, 2, 40) (dual of [(512, 2), 956, 41]-NRT-code), using algebraic-geometric NRT-code AG(2;F,983P) [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513 (see above)
  3. linear OOA(64⁶, 6, F₆₄, 2, 6) (dual of [(6, 2), 6, 7]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(64⁶, 64, F₆₄, 2, 6) (dual of [(64, 2), 122, 7]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;122,64) [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.