MinT - Information on Result #1026172

Information on Result #1026172

Linear OOA(3¹⁸⁷, 66, F₃, 3, 133) (dual of [(66, 3), 11, 134]-NRT-code), using juxtaposition based on

linear OOA(3²², 11, F₃, 3, 18) (dual of [(11, 3), 11, 19]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3²², 12, F₃, 3, 18) (dual of [(12, 3), 14, 19]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,17P) [i] based on function field F/F₃ with g(F) = 4 and N(F) ≥ 12, using
    - an explicitly constructive algebraic function field [i]
linear OOA(3¹⁵⁴, 55, F₃, 3, 114) (dual of [(55, 3), 11, 115]-NRT-code), using
- 3 step truncation [i] based on linear OOA(3¹⁵⁷, 56, F₃, 3, 117) (dual of [(56, 3), 11, 118]-NRT-code), using
  - repeating each code word 2 times [i] based on linear OOA(3⁷³, 28, F₃, 3, 58) (dual of [(28, 3), 11, 59]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,25P) [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28, 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(3¹⁸⁷, 66, F₃, 3, 132) (dual of [(66, 3), 11, 133]-NRT-code)	[i]		Strength Reduction for OOAs