MinT - Information on Result #912115

Information on Result #912115

Linear OOA(2²⁶⁰, 155, F₂, 2, 109) (dual of [(155, 2), 50, 110]-NRT-code), using concatenation of two NRT-codes based on

linear OA(32²¹, 31, F₃₂, 21) (dual of [31, 10, 22]-code or 31-arc in PG(20,32)), using
- discarding factors / shortening the dual code based on linear OA(32²¹, 32, F₃₂, 21) (dual of [32, 11, 22]-code or 32-arc in PG(20,32)), using
  - Reedâ€“Solomon code RS(11,32) [i]
linear OOA(2⁵, 5, F₂, 2, 4) (dual of [(5, 2), 5, 5]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,5P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, using
  - an explicitly constructive algebraic function field [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(2²⁶⁰, 155, F₂, 2, 108) (dual of [(155, 2), 50, 109]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(2²⁶⁰, 155, F₂, 2, 107) (dual of [(155, 2), 50, 108]-NRT-code)	[i]
3	Linear OOA(2²⁶⁰, 155, F₂, 2, 106) (dual of [(155, 2), 50, 107]-NRT-code)	[i]
4	Linear OOA(2²⁶⁰, 155, F₂, 2, 105) (dual of [(155, 2), 50, 106]-NRT-code)	[i]
5	Linear OOA(2²⁵⁹, 154, F₂, 2, 108) (dual of [(154, 2), 49, 109]-NRT-code)	[i]		Truncation for OOAs
6	Linear OOA(2²⁵⁸, 154, F₂, 2, 107) (dual of [(154, 2), 50, 108]-NRT-code)	[i]
7	Linear OOA(2²⁵⁷, 153, F₂, 2, 106) (dual of [(153, 2), 49, 107]-NRT-code)	[i]
8	Linear OOA(2²⁵⁶, 153, F₂, 2, 105) (dual of [(153, 2), 50, 106]-NRT-code)	[i]
9	Linear OOA(2²⁶⁰, 77, F₂, 4, 109) (dual of [(77, 4), 48, 110]-NRT-code)	[i]		OOA Folding