MinT - Information on Result #857606

Information on Result #857606

Linear OOA(16⁸³, 289, F₁₆, 2, 31) (dual of [(289, 2), 495, 32]-NRT-code), using OOA 2-folding based on linear OA(16⁸³, 578, F₁₆, 31) (dual of [578, 495, 32]-code), using

discarding factors / shortening the dual code based on linear OA(16⁸³, 579, F₁₆, 31) (dual of [579, 496, 32]-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OA(16²¹, 65, F₁₆, 15) (dual of [65, 44, 16]-code), using
    - extended algebraic-geometric code AG_e(F,49P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
      - the Hermitian function field over F₁₆ [i]
  2. linear OA(16⁶², 514, F₁₆, 31) (dual of [514, 452, 32]-code), using
    - trace code [i] based on linear OA(256³¹, 257, F₂₅₆, 31) (dual of [257, 226, 32]-code or 257-arc in PG(30,256)), using
      - extended Reedâ€“Solomon code RS_e(226,256) [i]
      - the expurgated narrow-sense BCH-code C(I) with length 257Â | 256²âˆ’1, defining interval IÂ =Â [0,15], and minimum distance dÂ â‰¥ |{−15,−14,…,15}|+1Â =Â 32 (BCH-bound) [i]
      - algebraic-geometric code AG(F, Q+111P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using the rational function field F₂₅₆(x) [i]
      - algebraic-geometric code AG(F,75P) with degPÂ =Â 3 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257 (see above)
      - algebraic-geometric code AG(F,45P) with degPÂ =Â 5 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257 (see above)

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.