MinT - Information on Result #1017860

Information on Result #1017860

Linear OOA(64⁸⁹, 5592547, F₆₄, 3, 14) (dual of [(5592547, 3), 16777552, 15]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(64²⁸, 2796266, F₆₄, 3, 7) (dual of [(2796266, 3), 8388770, 8]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(64³, 65, F₆₄, 3, 3) (dual of [(65, 3), 192, 4]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(3;192,64) [i]
  2. linear OOA(64²⁵, 2796201, F₆₄, 3, 7) (dual of [(2796201, 3), 8388578, 8]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(64²⁵, large, F₆₄, 7) (dual of [large, large−25, 8]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (BCH-bound) [i]
linear OOA(64⁶¹, 2796281, F₆₄, 3, 14) (dual of [(2796281, 3), 8388782, 15]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(64⁸, 80, F₆₄, 3, 7) (dual of [(80, 3), 232, 8]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,232P) [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
      - a function field by SÃ©mirat [i]
  2. linear OOA(64⁵³, 2796201, F₆₄, 3, 14) (dual of [(2796201, 3), 8388550, 15]-NRT-code), using
    - OOA 3-folding [i] 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.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

None.