MinT - Information on Result #1017804

Information on Result #1017804

Linear OOA(64⁸⁰, 5592547, F₆₄, 3, 13) (dual of [(5592547, 3), 16777561, 14]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(64²⁴, 2796266, F₆₄, 3, 6) (dual of [(2796266, 3), 8388774, 7]-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(64²¹, 2796201, F₆₄, 3, 6) (dual of [(2796201, 3), 8388582, 7]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(64²¹, large, F₆₄, 6) (dual of [large, large−21, 7]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 64⁴âˆ’1, defining interval IÂ =Â [0,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
linear OOA(64⁵⁶, 2796281, F₆₄, 3, 13) (dual of [(2796281, 3), 8388787, 14]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(64⁷, 80, F₆₄, 3, 6) (dual of [(80, 3), 233, 7]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,233P) [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(64⁴⁹, 2796201, F₆₄, 3, 13) (dual of [(2796201, 3), 8388554, 14]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(64⁴⁹, large, F₆₄, 13) (dual of [large, large−49, 14]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [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.