MinT - Information on Result #1028613

Information on Result #1028613

Linear OOA(2²⁴³, 93, F₂, 3, 125) (dual of [(93, 3), 36, 126]-NRT-code), using concatenation of two NRT-codes based on

linear OA(16²², 31, F₁₆, 20) (dual of [31, 9, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(16²², 33, F₁₆, 20) (dual of [33, 11, 21]-code), using
  - extended algebraic-geometric code AG_e(F,12P) [i] based on function field F/F₁₆ with g(F) = 2 and N(F) ≥ 33, using
    - a function field by SÃ©mirat [i]
linear OOA(2⁵, 3, F₂, 3, 5) (dual of [(3, 3), 4, 6]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(3;4,2) [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(2²⁴³, 93, F₂, 3, 124) (dual of [(93, 3), 36, 125]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(2²⁴³, 93, F₂, 3, 123) (dual of [(93, 3), 36, 124]-NRT-code)	[i]
3	Linear OOA(2²⁴³, 93, F₂, 3, 122) (dual of [(93, 3), 36, 123]-NRT-code)	[i]
4	Linear OOA(2²⁴³, 93, F₂, 3, 121) (dual of [(93, 3), 36, 122]-NRT-code)	[i]
5	Linear OOA(2²⁴⁴, 93, F₂, 3, 125) (dual of [(93, 3), 35, 126]-NRT-code)	[i]		OOA Duplication
6	Linear OOA(2²⁴⁵, 93, F₂, 3, 125) (dual of [(93, 3), 34, 126]-NRT-code)	[i]		OOA Duplication
7	Linear OOA(2²⁴², 92, F₂, 3, 124) (dual of [(92, 3), 34, 125]-NRT-code)	[i]		Truncation for OOAs
8	Linear OOA(2²⁴¹, 92, F₂, 3, 123) (dual of [(92, 3), 35, 124]-NRT-code)	[i]
9	Linear OOA(2²⁴⁰, 92, F₂, 3, 122) (dual of [(92, 3), 36, 123]-NRT-code)	[i]
10	Linear OOA(2²³⁹, 91, F₂, 3, 121) (dual of [(91, 3), 34, 122]-NRT-code)	[i]
11	Linear OOA(2²³⁸, 91, F₂, 3, 120) (dual of [(91, 3), 35, 121]-NRT-code)	[i]
12	Linear OOA(2²³⁷, 91, F₂, 3, 119) (dual of [(91, 3), 36, 120]-NRT-code)	[i]
13	Linear OOA(2²⁴³, 46, F₂, 6, 125) (dual of [(46, 6), 33, 126]-NRT-code)	[i]		OOA Folding