MinT - Information on Result #902003

Information on Result #902003

Linear OOA(32⁷⁸, 4194389, F₃₂, 2, 14) (dual of [(4194389, 2), 8388700, 15]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(32¹², 88, F₃₂, 2, 7) (dual of [(88, 2), 164, 8]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(32⁴, 1025, F₃₂, 2, 3) (dual of [(1025, 2), 2046, 4]-NRT-code), using
    - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(32⁴, 1025, F₃₂, 3) (dual of [1025, 1021, 4]-code or 1025-cap in PG(3,32)), using
      - ovoid in PG(3,Â 32) [i]
  2. linear OOA(32⁸, 44, F₃₂, 2, 7) (dual of [(44, 2), 80, 8]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,80P) [i] based on function field F/F₃₂ with g(F) = 1 and N(F) ≥ 44, using
      - a function field by SÃ©mirat [i]
linear OOA(32⁶⁶, 4194301, F₃₂, 2, 14) (dual of [(4194301, 2), 8388536, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OA(32⁶⁶, 8388602, F₃₂, 14) (dual of [8388602, 8388536, 15]-code), using
  - discarding factors / shortening the dual code based on linear OA(32⁶⁶, large, F₃₂, 14) (dual of [large, large−66, 15]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 33554431Â = 32⁵âˆ’1, defining interval IÂ =Â [0,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]

Mode: Constructive and linear.

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