MinT - Information on Result #669287

Information on Result #669287

Linear OA(49⁵², 5764854, F₄₉, 12) (dual of [5764854, 5764802, 13]-code), using (u,Â u+v)-construction based on

linear OA(49⁷, 53, F₄₉, 6) (dual of [53, 46, 7]-code), using
- constructionÂ X applied to AG(F, Q+20P) âŠ‚ AG(F, Q+21P) [i] based on
  1. linear OA(49⁶, 50, F₄₉, 6) (dual of [50, 44, 7]-code or 50-arc in PG(5,49)), using algebraic-geometric code AG(F, Q+20P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F₄₉ with g(F) = 0 and N(F) ≥ 50, using the rational function field F₄₉(x) [i]
  2. linear OA(49⁴, 50, F₄₉, 4) (dual of [50, 46, 5]-code or 50-arc in PG(3,49)), using algebraic-geometric code AG(F, Q+21P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F₄₉ with g(F) = 0 and N(F) ≥ 50 (see above)
  3. linear OA(49¹, 3, F₄₉, 1) (dual of [3, 2, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(49¹, s, F₄₉, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]
linear OA(49⁴⁵, 5764801, F₄₉, 12) (dual of [5764801, 5764756, 13]-code), using
- an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 49⁴âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]

Mode: Constructive and linear.

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