MinT - Information on Result #973079

Information on Result #973079

Linear OOA(5⁴⁴, 22, F₅, 3, 25) (dual of [(22, 3), 22, 26]-NRT-code), using OOA 2-folding based on linear OOA(5⁴⁴, 44, F₅, 2, 25) (dual of [(44, 2), 44, 26]-NRT-code), using

constructionÂ X applied to AG(2;F,29P) âŠ‚ AG(2;F,30P) [i] based on
1. linear OOA(5⁴², 42, F₅, 2, 25) (dual of [(42, 2), 42, 26]-NRT-code), using algebraic-geometric NRT-code AG(2;F,29P) with degPÂ =Â 2 [i] based on function field F/F₅ with g(F) = 17 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]
2. linear OOA(5⁴⁰, 42, F₅, 2, 23) (dual of [(42, 2), 44, 24]-NRT-code), using algebraic-geometric NRT-code AG(2;F,30P) with degPÂ =Â 2 [i] based on function field F/F₅ with g(F) = 17 and N(F) ≥ 42 (see above)
3. linear OOA(5², 2, F₅, 2, 1) (dual of [(2, 2), 2, 2]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(5², s, F₅, 2, 1) for arbitrarily large s, using
    - appending 1 arbitrary column [i] based on linear OA(5², s, F₅, 1) (dual of [s, s−2, 2]-code) for arbitrarily large s, using
      - 5¹ times duplication / taking a subcode [i] based on linear OA(5¹, s, F₅, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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.