MinT - Information on Result #666104

Information on Result #666104

Linear OA(25⁶⁵, 692, F₂₅, 25) (dual of [692, 627, 26]-code), using (u,Â u+v)-construction based on

linear OA(25¹⁷, 68, F₂₅, 12) (dual of [68, 51, 13]-code), using
- constructionÂ X applied to AG(F,52P) âŠ‚ AG(F,54P) [i] based on
  1. linear OA(25¹⁶, 65, F₂₅, 12) (dual of [65, 49, 13]-code), using algebraic-geometric code AG(F,52P) [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(25¹⁴, 65, F₂₅, 10) (dual of [65, 51, 11]-code), using algebraic-geometric code AG(F,54P) [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(25⁴⁸, 624, F₂₅, 25) (dual of [624, 576, 26]-code), using
- the primitive narrow-sense BCH-code C(I) with length 624Â = 25²âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]

Mode: Constructive and linear.

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