MinT - Information on Result #1021210

Information on Result #1021210

Linear OOA(4²³⁰, 80, F₄, 3, 179) (dual of [(80, 3), 10, 180]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(4⁵¹, 20, F₄, 3, 44) (dual of [(20, 3), 9, 45]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4⁵¹, 21, F₄, 3, 44) (dual of [(21, 3), 12, 45]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,18P) [i] based on function field F/F₄ with g(F) = 7 and N(F) ≥ 21, using
    - an explicitly constructive algebraic function field [i]
linear OOA(4⁵⁹, 20, F₄, 3, 59) (dual of [(20, 3), 1, 60]-NRT-code), using
- dual of repetition NRT-code with length 20 [i]
linear OOA(4⁶⁰, 20, F₄, 3, 60) (dual of [(20, 3), 0, 61]-NRT-code), using
- complete OOA / dual of NRT-code with only one code word [i]
linear OOA(4⁶⁰, 20, F₄, 3, 60) (dual of [(20, 3), 0, 61]-NRT-code) (see above)

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(4²³⁰, 80, F₄, 3, 178) (dual of [(80, 3), 10, 179]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(4²³⁰, 80, F₄, 3, 177) (dual of [(80, 3), 10, 178]-NRT-code)	[i]		Strength Reduction for OOAs