MinT - Information on Result #666058

Information on Result #666058

Linear OA(25⁶⁸, 693, F₂₅, 27) (dual of [693, 625, 28]-code), using (u,Â u+v)-construction based on

linear OA(25¹⁸, 68, F₂₅, 13) (dual of [68, 50, 14]-code), using
- constructionÂ X applied to AG(F,51P) âŠ‚ AG(F,53P) [i] based on
  1. linear OA(25¹⁷, 65, F₂₅, 13) (dual of [65, 48, 14]-code), using algebraic-geometric code AG(F,51P) [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
    - a function field by GarcÃa and Quoos [i]
  2. linear OA(25¹⁵, 65, F₂₅, 11) (dual of [65, 50, 12]-code), using algebraic-geometric code AG(F,53P) [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66 (see above)
  3. linear OA(25¹, 3, F₂₅, 1) (dual of [3, 2, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(25¹, s, F₂₅, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]
linear OA(25⁵⁰, 625, F₂₅, 27) (dual of [625, 575, 28]-code), using
- an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 624Â = 25²âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]

Mode: Constructive and linear.

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