MinT - Information on Result #906181

Information on Result #906181

Linear OOA(3³¹, 18, F₃, 2, 23) (dual of [(18, 2), 5, 24]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(3⁸, 6, F₃, 2, 7) (dual of [(6, 2), 4, 8]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3⁸, 7, F₃, 2, 7) (dual of [(7, 2), 6, 8]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,6P) [i] based on function field F/F₃ with g(F) = 1 and N(F) ≥ 7, using
    - an explicitly constructive algebraic function field [i]
linear OOA(3¹¹, 6, F₃, 2, 11) (dual of [(6, 2), 1, 12]-NRT-code), using
- dual of repetition NRT-code with length 6 [i]
linear OOA(3¹², 6, F₃, 2, 12) (dual of [(6, 2), 0, 13]-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		Method
1	Linear OOA(3²⁹, 17, F₃, 2, 21) (dual of [(17, 2), 5, 22]-NRT-code)	[i]	Truncation for OOAs
2	Linear OOA(3¹⁷⁵, 90, F₃, 2, 119) (dual of [(90, 2), 5, 120]-NRT-code)	[i]	Repeating Each Code Word for NRT-Codes
3	Linear OOA(3²⁴⁷, 126, F₃, 2, 167) (dual of [(126, 2), 5, 168]-NRT-code)	[i]	Repeating Each Code Word for NRT-Codes
4	Linear OOA(3⁴⁵, 25, F₃, 2, 32) (dual of [(25, 2), 5, 33]-NRT-code)	[i]	Juxtaposition for OOAs
5	Linear OOA(3¹⁰¹, 53, F₃, 2, 70) (dual of [(53, 2), 5, 71]-NRT-code)	[i]
6	Linear OOA(3¹⁰⁷, 56, F₃, 2, 74) (dual of [(56, 2), 5, 75]-NRT-code)	[i]
7	Linear OOA(3¹²⁵, 65, F₃, 2, 86) (dual of [(65, 2), 5, 87]-NRT-code)	[i]
8	Linear OOA(3¹³¹, 68, F₃, 2, 90) (dual of [(68, 2), 5, 91]-NRT-code)	[i]
9	Linear OOA(3²⁴¹, 123, F₃, 2, 164) (dual of [(123, 2), 5, 165]-NRT-code)	[i]
10	Linear OOA(3³¹, 9, F₃, 4, 23) (dual of [(9, 4), 5, 24]-NRT-code)	[i]	OOA Folding