MinT - Information on Result #1028905

Information on Result #1028905

Linear OOA(2²⁵⁴, 108, F₂, 3, 109) (dual of [(108, 3), 70, 110]-NRT-code), using concatenation of two NRT-codes based on

linear OA(32²², 36, F₃₂, 21) (dual of [36, 14, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(32²², 43, F₃₂, 21) (dual of [43, 21, 22]-code), using
  - algebraic-geometric code AG(F,21P) [i] based on function field F/F₃₂ with g(F) = 1 and N(F) ≥ 44, using
    - a function field by SÃ©mirat [i]
linear OOA(2⁴, 3, F₂, 3, 4) (dual of [(3, 3), 5, 5]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(3;5,2) [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(2²⁵⁴, 108, F₂, 3, 108) (dual of [(108, 3), 70, 109]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(2²⁵⁴, 108, F₂, 3, 107) (dual of [(108, 3), 70, 108]-NRT-code)	[i]
3	Linear OOA(2²⁵⁴, 108, F₂, 3, 106) (dual of [(108, 3), 70, 107]-NRT-code)	[i]
4	Linear OOA(2²⁵⁷, 109, F₂, 3, 109) (dual of [(109, 3), 70, 110]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
5	Linear OOA(2²⁵⁵, 108, F₂, 3, 109) (dual of [(108, 3), 69, 110]-NRT-code)	[i]	OOA Duplication
6	Linear OOA(2²⁵⁶, 108, F₂, 3, 109) (dual of [(108, 3), 68, 110]-NRT-code)	[i]	OOA Duplication
7	Linear OOA(2²⁵³, 107, F₂, 3, 108) (dual of [(107, 3), 68, 109]-NRT-code)	[i]	Truncation for OOAs
8	Linear OOA(2²⁵², 107, F₂, 3, 107) (dual of [(107, 3), 69, 108]-NRT-code)	[i]
9	Linear OOA(2²⁵¹, 107, F₂, 3, 106) (dual of [(107, 3), 70, 107]-NRT-code)	[i]
10	Linear OOA(2²⁵⁰, 106, F₂, 3, 105) (dual of [(106, 3), 68, 106]-NRT-code)	[i]
11	Linear OOA(2²⁵⁴, 54, F₂, 6, 109) (dual of [(54, 6), 70, 110]-NRT-code)	[i]	OOA Folding