MinT - Information on Result #1117690

Information on Result #1117690

Linear OOA(3²³⁷, 3355456, F₃, 5, 16) (dual of [(3355456, 5), 16777043, 17]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3⁷⁶, 2097150, F₃, 5, 8) (dual of [(2097150, 5), 10485674, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(3⁷⁶, 8388600, F₃, 8) (dual of [8388600, 8388524, 9]-code), using
  - discarding factors / shortening the dual code based on linear OA(3⁷⁶, large, F₃, 8) (dual of [large, large−76, 9]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
linear OOA(3¹⁶¹, 1677728, F₃, 5, 16) (dual of [(1677728, 5), 8388479, 17]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3¹⁰, 8, F₃, 5, 8) (dual of [(8, 5), 30, 9]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(5;F,31P) [i] based on function field F/F₃ with g(F) = 2 and N(F) ≥ 8, using
      - an explicitly constructive algebraic function field [i]
  2. linear OOA(3¹⁵¹, 1677720, F₃, 5, 16) (dual of [(1677720, 5), 8388449, 17]-NRT-code), using
    - OOA 5-folding [i] based on linear OA(3¹⁵¹, 8388600, F₃, 16) (dual of [8388600, 8388449, 17]-code), using
      - discarding factors / shortening the dual code based on linear OA(3¹⁵¹, large, F₃, 16) (dual of [large, large−151, 17]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [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.