MinT - Information on Result #908569

Information on Result #908569

Linear OOA(2²⁰⁴, 106, F₂, 2, 105) (dual of [(106, 2), 8, 106]-NRT-code), using juxtaposition based on

linear OOA(2⁶², 35, F₂, 2, 33) (dual of [(35, 2), 8, 34]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2⁶², 36, F₂, 2, 33) (dual of [(36, 2), 10, 34]-NRT-code), using
  - concatenation of two NRT-codes [i] based on
    1. linear OOA(4¹⁹, 12, F₄, 2, 16) (dual of [(12, 2), 5, 17]-NRT-code), using
      - discarding factors / shortening the dual code based on linear OOA(4¹⁹, 14, F₄, 2, 16) (dual of [(14, 2), 9, 17]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(2;F,11P) [i] based on function field F/F₄ with g(F) = 3 and N(F) ≥ 14, using
        an explicitly constructive algebraic function field [i]
    2. linear OA(2¹, 3, F₂, 1) (dual of [3, 2, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
linear OOA(2¹³⁴, 71, F₂, 2, 71) (dual of [(71, 2), 8, 72]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2⁶³, 35, F₂, 2, 35) (dual of [(35, 2), 7, 36]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(2²⁸, 17, F₂, 2, 17) (dual of [(17, 2), 6, 18]-NRT-code), using
        (u,Â u+v)-construction [i] based on
        linear OOA(2¹¹, 8, F₂, 2, 8) (dual of [(8, 2), 5, 9]-NRT-code), using
        an explicit generator matrix by Edel [i]
        linear OOA(2¹⁷, 9, F₂, 2, 17) (dual of [(9, 2), 1, 18]-NRT-code), using
        dual of repetition NRT-code with length 9 [i]
      2. linear OOA(2³⁵, 18, F₂, 2, 35) (dual of [(18, 2), 1, 36]-NRT-code), using
        dual of repetition NRT-code with length 18 [i]
  2. linear OOA(2⁷¹, 36, F₂, 2, 71) (dual of [(36, 2), 1, 72]-NRT-code), using
    - dual of repetition NRT-code with length 36 [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.