MinT - Information on Result #1084549

Information on Result #1084549

Linear OOA(3²²⁷, 76, F₃, 4, 115) (dual of [(76, 4), 77, 116]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(3⁵¹, 24, F₃, 4, 38) (dual of [(24, 4), 45, 39]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(4;F,57P) [i] based on function field F/F₃ with g(F) = 13 and N(F) ≥ 24, using
  - a function field by SÃ©mirat [i]
linear OOA(3⁷², 26, F₃, 4, 57) (dual of [(26, 4), 32, 58]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3⁷², 28, F₃, 4, 57) (dual of [(28, 4), 40, 58]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(4;F,54P) [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28, using
    - an explicitly constructive algebraic function field [i]
linear OOA(3¹⁰⁴, 26, F₃, 4, 104) (dual of [(26, 4), 0, 105]-NRT-code), using
- complete OOA / dual of NRT-code with only one code word [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3²²⁷, 76, F₃, 4, 114) (dual of [(76, 4), 77, 115]-NRT-code)	[i]		Strength Reduction for OOAs