MinT - Information on Result #2428283

Information on Result #2428283

Linear OOA(2²⁴⁵, 150, F₂, 2, 98) (dual of [(150, 2), 55, 99]-NRT-code), using strength reduction based on linear OOA(2²⁴⁵, 150, F₂, 2, 99) (dual of [(150, 2), 55, 100]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(32¹⁹, 30, F₃₂, 19) (dual of [30, 11, 20]-code or 30-arc in PG(18,32)), using
  - discarding factors / shortening the dual code based on linear OA(32¹⁹, 32, F₃₂, 19) (dual of [32, 13, 20]-code or 32-arc in PG(18,32)), using
    - Reedâ€“Solomon code RS(13,32) [i]
2. 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		Method
1	Linear OOA(2²⁴⁷, 151, F₂, 2, 98) (dual of [(151, 2), 55, 99]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(2²⁴⁶, 150, F₂, 2, 98) (dual of [(150, 2), 54, 99]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2²⁴⁴, 149, F₂, 2, 97) (dual of [(149, 2), 54, 98]-NRT-code)	[i]	Truncation for OOAs
4	Linear OOA(2²⁴³, 149, F₂, 2, 96) (dual of [(149, 2), 55, 97]-NRT-code)	[i]
5	Linear OOA(2²⁴², 148, F₂, 2, 95) (dual of [(148, 2), 54, 96]-NRT-code)	[i]
6	Linear OOA(2²⁴⁵, 75, F₂, 4, 98) (dual of [(75, 4), 55, 99]-NRT-code)	[i]	OOA Folding