MinT - Information on Result #900310

Information on Result #900310

Linear OOA(25¹⁰⁴, 444, F₂₅, 2, 38) (dual of [(444, 2), 784, 39]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(25²⁹, 126, F₂₅, 2, 19) (dual of [(126, 2), 223, 20]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,232P) [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126, using
  - the Hermitian function field over F₂₅ [i]
linear OOA(25⁷⁵, 318, F₂₅, 2, 38) (dual of [(318, 2), 561, 39]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25⁷⁵, 636, F₂₅, 38) (dual of [636, 561, 39]-code), using
  - constructionÂ X applied to C_e(37) âŠ‚ C_e(33) [i] based on
    1. linear OA(25⁷², 625, F₂₅, 38) (dual of [625, 553, 39]-code), using an extension C_e(37) of the primitive narrow-sense BCH-code C(I) with length 624Â = 25²âˆ’1, defining interval IÂ =Â [1,37], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 38 [i]
    2. linear OA(25⁶⁴, 625, F₂₅, 34) (dual of [625, 561, 35]-code), using an extension C_e(33) of the primitive narrow-sense BCH-code C(I) with length 624Â = 25²âˆ’1, defining interval IÂ =Â [1,33], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 34 [i]
    3. linear OA(25³, 11, F₂₅, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,25) or 11-cap in PG(2,25)), using
      - discarding factors / shortening the dual code based on linear OA(25³, 25, F₂₅, 3) (dual of [25, 22, 4]-code or 25-arc in PG(2,25) or 25-cap in PG(2,25)), using
        Reedâ€“Solomon code RS(22,25) [i]

Mode: Constructive and linear.

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