MinT - Information on Result #912881

Information on Result #912881

Linear OOA(3²²², 120, F₃, 2, 143) (dual of [(120, 2), 18, 144]-NRT-code), using concatenation of two NRT-codes based on

linear OA(27²⁴, 30, F₂₇, 23) (dual of [30, 6, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(27²⁴, 38, F₂₇, 23) (dual of [38, 14, 24]-code), using
  - extended algebraic-geometric code AG_e(F,14P) [i] based on function field F/F₂₇ with g(F) = 1 and N(F) ≥ 38, using
    - a function field by SÃ©mirat [i]
linear OOA(3⁵, 4, F₃, 2, 5) (dual of [(4, 2), 3, 6]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(2;3,3) [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3²²², 120, F₃, 2, 142) (dual of [(120, 2), 18, 143]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(3²²², 120, F₃, 2, 141) (dual of [(120, 2), 18, 142]-NRT-code)	[i]		Strength Reduction for OOAs
3	Linear OOA(3²²³, 120, F₃, 2, 143) (dual of [(120, 2), 17, 144]-NRT-code)	[i]		OOA Duplication
4	Linear OOA(3²²¹, 119, F₃, 2, 142) (dual of [(119, 2), 17, 143]-NRT-code)	[i]		Truncation for OOAs
5	Linear OOA(3²²⁰, 119, F₃, 2, 141) (dual of [(119, 2), 18, 142]-NRT-code)	[i]
6	Linear OOA(3²¹⁹, 118, F₃, 2, 140) (dual of [(118, 2), 17, 141]-NRT-code)	[i]
7	Linear OOA(3²¹⁸, 118, F₃, 2, 139) (dual of [(118, 2), 18, 140]-NRT-code)	[i]
8	Linear OOA(3²¹⁷, 117, F₃, 2, 138) (dual of [(117, 2), 17, 139]-NRT-code)	[i]
9	Linear OOA(3²¹⁶, 117, F₃, 2, 137) (dual of [(117, 2), 18, 138]-NRT-code)	[i]
10	Linear OOA(3²¹⁵, 116, F₃, 2, 136) (dual of [(116, 2), 17, 137]-NRT-code)	[i]
11	Linear OOA(3²¹⁴, 116, F₃, 2, 135) (dual of [(116, 2), 18, 136]-NRT-code)	[i]
12	Linear OOA(3²²², 60, F₃, 4, 143) (dual of [(60, 4), 18, 144]-NRT-code)	[i]		OOA Folding