MinT - Information on Result #1084430

Information on Result #1084430

Linear OOA(3²⁴¹, 75, F₃, 4, 134) (dual of [(75, 4), 59, 135]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(3⁵⁹, 25, F₃, 4, 44) (dual of [(25, 4), 41, 45]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3⁵⁹, 28, F₃, 4, 44) (dual of [(28, 4), 53, 45]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(4;F,67P) [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(3⁸², 25, F₃, 4, 67) (dual of [(25, 4), 18, 68]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3⁸², 28, F₃, 4, 67) (dual of [(28, 4), 30, 68]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(4;F,44P) [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28 (see above)
linear OOA(3¹⁰⁰, 25, F₃, 4, 100) (dual of [(25, 4), 0, 101]-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(3²⁴¹, 75, F₃, 4, 133) (dual of [(75, 4), 59, 134]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(3²⁴¹, 75, F₃, 4, 132) (dual of [(75, 4), 59, 133]-NRT-code)	[i]		Strength Reduction for OOAs