MinT - Information on Result #1121216

Information on Result #1121216

Linear OOA(3²⁵⁰, 51, F₃, 5, 217) (dual of [(51, 5), 5, 218]-NRT-code), using juxtaposition based on

linear OOA(3²⁰, 5, F₃, 5, 19) (dual of [(5, 5), 5, 20]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3²⁰, 7, F₃, 5, 19) (dual of [(7, 5), 15, 20]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(5;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]
linear OOA(3²²⁵, 46, F₃, 5, 197) (dual of [(46, 5), 5, 198]-NRT-code), using
- strength reduction [i] based on linear OOA(3²²⁵, 46, F₃, 5, 198) (dual of [(46, 5), 5, 199]-NRT-code), using
  - juxtaposition [i] based on
    1. linear OOA(3⁴⁵, 10, F₃, 5, 42) (dual of [(10, 5), 5, 43]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(5;F,7P) [i] based on function field F/F₃ with g(F) = 3 and N(F) ≥ 10, using
        an explicitly constructive algebraic function field [i]
    2. linear OOA(3¹⁷⁵, 36, F₃, 5, 155) (dual of [(36, 5), 5, 156]-NRT-code), using
      - repeating each code word 3 times [i] based on linear OOA(3⁵⁵, 12, F₃, 5, 51) (dual of [(12, 5), 5, 52]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(5;F,8P) [i] based on function field F/F₃ with g(F) = 4 and N(F) ≥ 12, using
        an explicitly constructive algebraic function field [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3²⁵⁰, 51, F₃, 5, 216) (dual of [(51, 5), 5, 217]-NRT-code)	[i]		Strength Reduction for OOAs