MinT - Information on Result #903701

Information on Result #903701

Linear OOA(64⁶⁵, 4194461, F₆₄, 2, 14) (dual of [(4194461, 2), 8388857, 15]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(64¹², 160, F₆₄, 2, 7) (dual of [(160, 2), 308, 8]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(64⁴, 4097, F₆₄, 2, 3) (dual of [(4097, 2), 8190, 4]-NRT-code), using
    - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(64⁴, 4097, F₆₄, 3) (dual of [4097, 4093, 4]-code or 4097-cap in PG(3,64)), using
      - ovoid in PG(3,Â 64) [i]
  2. linear OOA(64⁸, 80, F₆₄, 2, 7) (dual of [(80, 2), 152, 8]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,152P) [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
      - a function field by SÃ©mirat [i]
linear OOA(64⁵³, 4194301, F₆₄, 2, 14) (dual of [(4194301, 2), 8388549, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OA(64⁵³, 8388602, F₆₄, 14) (dual of [8388602, 8388549, 15]-code), using
  - discarding factors / shortening the dual code based on linear OA(64⁵³, large, F₆₄, 14) (dual of [large, large−53, 15]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 64⁴âˆ’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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