MinT - Information on Result #1101085

Information on Result #1101085

Linear OOA(3²¹⁷, 2796204, F₃, 5, 15) (dual of [(2796204, 5), 13980803, 16]-NRT-code), using OOA 2-folding based on linear OOA(3²¹⁷, 5592408, F₃, 3, 15) (dual of [(5592408, 3), 16777007, 16]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3²¹⁷, 5592409, F₃, 3, 15) (dual of [(5592409, 3), 16777010, 16]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(3⁶, 7, F₃, 3, 5) (dual of [(7, 3), 15, 6]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,15P) [i] based on function field F/F₃ with g(F) = 1 and N(F) ≥ 7, using
      - an explicitly constructive algebraic function field [i]
  2. linear OOA(3⁶¹, 2796201, F₃, 3, 7) (dual of [(2796201, 3), 8388542, 8]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(3⁶¹, large, F₃, 7) (dual of [large, large−61, 8]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 14348908Â | 3³⁰âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (BCH-bound) [i]
  3. linear OOA(3¹⁵⁰, 2796201, F₃, 3, 15) (dual of [(2796201, 3), 8388453, 16]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(3¹⁵⁰, large, F₃, 15) (dual of [large, large−150, 16]-code), using
      - the primitive narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [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.