MinT - Information on Result #2767487

Information on Result #2767487

Linear OOA(2²⁴⁸, 65, F₂, 4, 168) (dual of [(65, 4), 12, 169]-NRT-code), using strength reduction based on linear OOA(2²⁴⁸, 65, F₂, 4, 175) (dual of [(65, 4), 12, 176]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(16¹⁰, 13, F₁₆, 10) (dual of [13, 3, 11]-code or 13-arc in PG(9,16)), using
  - discarding factors / shortening the dual code based on linear OA(16¹⁰, 16, F₁₆, 10) (dual of [16, 6, 11]-code or 16-arc in PG(9,16)), using
    - Reedâ€“Solomon code RS(6,16) [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(2²⁴⁶, 64, F₂, 4, 166) (dual of [(64, 4), 10, 167]-NRT-code)	[i]	Truncation for OOAs
2	Linear OOA(2²⁴⁵, 64, F₂, 4, 165) (dual of [(64, 4), 11, 166]-NRT-code)	[i]
3	Linear OOA(2²⁴², 63, F₂, 4, 162) (dual of [(63, 4), 10, 163]-NRT-code)	[i]
4	Linear OOA(2²⁴¹, 63, F₂, 4, 161) (dual of [(63, 4), 11, 162]-NRT-code)	[i]
5	Linear OOA(2²³⁷, 62, F₂, 4, 157) (dual of [(62, 4), 11, 158]-NRT-code)	[i]
6	Linear OOA(2²³⁶, 62, F₂, 4, 156) (dual of [(62, 4), 12, 157]-NRT-code)	[i]
7	Linear OOA(2²³², 61, F₂, 4, 152) (dual of [(61, 4), 12, 153]-NRT-code)	[i]