MinT - Information on Result #2622177

Information on Result #2622177

Linear OOA(3¹²⁵, 43, F₃, 3, 99) (dual of [(43, 3), 4, 100]-NRT-code), using strength reduction based on linear OOA(3¹²⁵, 43, F₃, 3, 102) (dual of [(43, 3), 4, 103]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(3⁸, 4, F₃, 3, 8) (dual of [(4, 3), 4, 9]-NRT-code), using
  - extended Reedâ€“Solomon NRT-code RS_e(3;4,3) [i]
2. linear OOA(3¹¹³, 39, F₃, 3, 93) (dual of [(39, 3), 4, 94]-NRT-code), using
  - juxtaposition [i] based on
    1. linear OOA(3⁸, 4, F₃, 3, 8) (dual of [(4, 3), 4, 9]-NRT-code) (see above)
    2. linear OOA(3¹⁰¹, 35, F₃, 3, 84) (dual of [(35, 3), 4, 85]-NRT-code), using
      - repeating each code word 5 times [i] based on linear OOA(3¹⁷, 7, F₃, 3, 16) (dual of [(7, 3), 4, 17]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(3;F,4P) [i] based on function field F/F₃ with g(F) = 1 and N(F) ≥ 7, using
        an explicitly constructive algebraic function field [i]

Mode: Constructive and linear.

Optimality

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

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3²¹³, 84, F₃, 3, 99) (dual of [(84, 3), 39, 100]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs