MinT - Information on Result #942131

Information on Result #942131

Linear OOA(4²⁵⁶, 201, F₄, 2, 105) (dual of [(201, 2), 146, 106]-NRT-code), using concatenation of two NRT-codes based on

linear OOA(16⁶¹, 67, F₁₆, 2, 52) (dual of [(67, 2), 73, 53]-NRT-code), using
- constructionÂ X applied to AG(2;F,75P) âŠ‚ AG(2;F,79P) [i] based on
  1. linear OOA(16⁵⁸, 64, F₁₆, 2, 52) (dual of [(64, 2), 70, 53]-NRT-code), using algebraic-geometric NRT-code AG(2;F,75P) [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 OOA(16⁵⁴, 64, F₁₆, 2, 48) (dual of [(64, 2), 74, 49]-NRT-code), using algebraic-geometric NRT-code AG(2;F,79P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65 (see above)
  3. linear OOA(16³, 3, F₁₆, 2, 3) (dual of [(3, 2), 3, 4]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(16³, 16, F₁₆, 2, 3) (dual of [(16, 2), 29, 4]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;29,16) [i]
linear OA(4¹, 3, F₄, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(4¹, s, F₄, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
  - parity-check code [i]

Mode: Constructive and linear.

None.

The following results depend on this result: