MinT - Information on Result #661702

Information on Result #661702

Linear OA(16¹³⁰, 145, F₁₆, 96) (dual of [145, 15, 97]-code), using juxtaposition based on

linear OA(16⁴⁸, 63, F₁₆, 42) (dual of [63, 15, 43]-code), using
- discarding factors / shortening the dual code based on linear OA(16⁴⁸, 64, F₁₆, 42) (dual of [64, 16, 43]-code), using
  - algebraic-geometric code AG(F,21P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
    - the Hermitian function field over F₁₆ [i]
linear OA(16⁶⁷, 82, F₁₆, 53) (dual of [82, 15, 54]-code), using
- constructionÂ XX applied to AG(F,10P) âŠ‚ AG(F,19P) âŠ‚ AG(F,20P) [i] based on
  1. linear OA(16⁵⁸, 64, F₁₆, 53) (dual of [64, 6, 54]-code), using algebraic-geometric code AG(F,10P) with known gap numbers [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(16⁵⁰, 64, F₁₆, 44) (dual of [64, 14, 45]-code), using algebraic-geometric code AG(F,19P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65 (see above)
  3. linear OA(16⁴⁹, 64, F₁₆, 43) (dual of [64, 15, 44]-code), using algebraic-geometric code AG(F,20P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65 (see above)
  4. linear OA(16⁸, 17, F₁₆, 8) (dual of [17, 9, 9]-code or 17-arc in PG(7,16)), using
    - extended Reedâ€“Solomon code RS_e(9,16) [i]
  5. linear OA(16⁰, 1, F₁₆, 0) (dual of [1, 1, 1]-code), using
    - dual of repetition code with length 1 [i]

Mode: Constructive and linear.

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