MinT - Information on Result #990287

Information on Result #990287

Linear OOA(64⁶⁹, 258, F₆₄, 3, 37) (dual of [(258, 3), 705, 38]-NRT-code), using OOA 2-folding based on linear OOA(64⁶⁹, 516, F₆₄, 2, 37) (dual of [(516, 2), 963, 38]-NRT-code), using

constructionÂ X applied to AG(2;F,986P) âŠ‚ AG(2;F,991P) [i] based on
1. linear OOA(64⁶⁵, 512, F₆₄, 2, 37) (dual of [(512, 2), 959, 38]-NRT-code), using algebraic-geometric NRT-code AG(2;F,986P) [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
  - the Hermitian function field over F₆₄ [i]
2. linear OOA(64⁶⁰, 512, F₆₄, 2, 32) (dual of [(512, 2), 964, 33]-NRT-code), using algebraic-geometric NRT-code AG(2;F,991P) [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513 (see above)
3. linear OOA(64⁴, 4, F₆₄, 2, 4) (dual of [(4, 2), 4, 5]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(64⁴, 64, F₆₄, 2, 4) (dual of [(64, 2), 124, 5]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(2;124,64) [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.