MinT - Information on Result #912880

Information on Result #912880

Linear OOA(3²²⁷, 124, F₃, 2, 143) (dual of [(124, 2), 21, 144]-NRT-code), using concatenation of two NRT-codes based on

linear OA(27²⁴, 31, F₂₇, 23) (dual of [31, 7, 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(3²²⁷, 124, F₃, 2, 142) (dual of [(124, 2), 21, 143]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(3²²⁷, 124, F₃, 2, 141) (dual of [(124, 2), 21, 142]-NRT-code)	[i]
3	Linear OOA(3²²⁷, 124, F₃, 2, 140) (dual of [(124, 2), 21, 141]-NRT-code)	[i]
4	Linear OOA(3²²⁷, 124, F₃, 2, 139) (dual of [(124, 2), 21, 140]-NRT-code)	[i]
5	Linear OOA(3²²⁸, 124, F₃, 2, 143) (dual of [(124, 2), 20, 144]-NRT-code)	[i]		OOA Duplication
6	Linear OOA(3²²⁶, 123, F₃, 2, 142) (dual of [(123, 2), 20, 143]-NRT-code)	[i]		Truncation for OOAs
7	Linear OOA(3²²⁵, 123, F₃, 2, 141) (dual of [(123, 2), 21, 142]-NRT-code)	[i]
8	Linear OOA(3²²⁴, 122, F₃, 2, 140) (dual of [(122, 2), 20, 141]-NRT-code)	[i]
9	Linear OOA(3²²³, 122, F₃, 2, 139) (dual of [(122, 2), 21, 140]-NRT-code)	[i]
10	Linear OOA(3²²², 121, F₃, 2, 138) (dual of [(121, 2), 20, 139]-NRT-code)	[i]
11	Linear OOA(3²²¹, 121, F₃, 2, 137) (dual of [(121, 2), 21, 138]-NRT-code)	[i]
12	Linear OOA(3²²⁷, 62, F₃, 4, 143) (dual of [(62, 4), 21, 144]-NRT-code)	[i]		OOA Folding