MinT - Information on Result #2451045

Information on Result #2451045

Linear OOA(8¹⁶³, 84, F₈, 2, 144) (dual of [(84, 2), 5, 145]-NRT-code), using strength reduction based on linear OOA(8¹⁶³, 84, F₈, 2, 145) (dual of [(84, 2), 5, 146]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(8¹⁵, 10, F₈, 2, 14) (dual of [(10, 2), 5, 15]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(8¹⁵, 14, F₈, 2, 14) (dual of [(14, 2), 13, 15]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,13P) [i] based on function field F/F₈ with g(F) = 1 and N(F) ≥ 14, using
      - F₂ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]
2. linear OOA(8¹⁴³, 74, F₈, 2, 130) (dual of [(74, 2), 5, 131]-NRT-code), using
  - juxtaposition [i] based on
    1. linear OOA(8¹³, 9, F₈, 2, 13) (dual of [(9, 2), 5, 14]-NRT-code), using
      - extended Reedâ€“Solomon NRT-code RS_e(2;5,8) [i]
    2. linear OOA(8¹²⁵, 65, F₈, 2, 116) (dual of [(65, 2), 5, 117]-NRT-code), using
      - standard lengthening with (d₀,â€¦,d₁)Â = (115,116) [i] based on linear OOA(8¹²³, 64, F₈, 2, 114) (dual of [(64, 2), 5, 115]-NRT-code), using algebraic-geometric NRT-code AG(2;F,13P) with known gap numbers [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using the Suzuki function field over F₈ [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.