MinT - Information on Result #1084542

Information on Result #1084542

Linear OOA(3²³⁴, 81, F₃, 4, 116) (dual of [(81, 4), 90, 117]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(3⁵³, 27, F₃, 4, 38) (dual of [(27, 4), 55, 39]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3⁵³, 28, F₃, 4, 38) (dual of [(28, 4), 59, 39]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(4;F,73P) [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(3⁷³, 27, F₃, 4, 58) (dual of [(27, 4), 35, 59]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3⁷³, 28, F₃, 4, 58) (dual of [(28, 4), 39, 59]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(4;F,53P) [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28 (see above)
linear OOA(3¹⁰⁸, 27, F₃, 4, 108) (dual of [(27, 4), 0, 109]-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(3²³⁴, 81, F₃, 4, 115) (dual of [(81, 4), 90, 116]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(3²³⁴, 81, F₃, 4, 114) (dual of [(81, 4), 90, 115]-NRT-code)	[i]		Strength Reduction for OOAs