MinT - Information on Result #2767209

Information on Result #2767209

Linear OOA(2²⁴⁴, 65, F₂, 4, 158) (dual of [(65, 4), 16, 159]-NRT-code), using strength reduction based on linear OOA(2²⁴⁴, 65, F₂, 4, 159) (dual of [(65, 4), 16, 160]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(16⁹, 13, F₁₆, 9) (dual of [13, 4, 10]-code or 13-arc in PG(8,16)), using
  - discarding factors / shortening the dual code based on linear OA(16⁹, 16, F₁₆, 9) (dual of [16, 7, 10]-code or 16-arc in PG(8,16)), using
    - Reedâ€“Solomon code RS(7,16) [i]
2. linear OOA(2¹⁶, 5, F₂, 4, 15) (dual of [(5, 4), 4, 16]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(4;F,4P) [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(2²⁴³, 64, F₂, 4, 157) (dual of [(64, 4), 13, 158]-NRT-code)	[i]	Truncation for OOAs
2	Linear OOA(2²⁴², 64, F₂, 4, 156) (dual of [(64, 4), 14, 157]-NRT-code)	[i]
3	Linear OOA(2²⁴¹, 64, F₂, 4, 155) (dual of [(64, 4), 15, 156]-NRT-code)	[i]
4	Linear OOA(2²³⁹, 63, F₂, 4, 153) (dual of [(63, 4), 13, 154]-NRT-code)	[i]
5	Linear OOA(2²³⁸, 63, F₂, 4, 152) (dual of [(63, 4), 14, 153]-NRT-code)	[i]
6	Linear OOA(2²³⁷, 63, F₂, 4, 151) (dual of [(63, 4), 15, 152]-NRT-code)	[i]
7	Linear OOA(2²³³, 62, F₂, 4, 147) (dual of [(62, 4), 15, 148]-NRT-code)	[i]
8	Linear OOA(2²³², 62, F₂, 4, 146) (dual of [(62, 4), 16, 147]-NRT-code)	[i]
9	Linear OOA(2²²⁹, 61, F₂, 4, 143) (dual of [(61, 4), 15, 144]-NRT-code)	[i]
10	Linear OOA(2²²⁸, 61, F₂, 4, 142) (dual of [(61, 4), 16, 143]-NRT-code)	[i]