MinT - Information on Result #911224

Information on Result #911224

Linear OOA(2¹²⁹, 72, F₂, 2, 67) (dual of [(72, 2), 15, 68]-NRT-code), using concatenation of two NRT-codes based on

linear OA(8¹⁹, 24, F₈, 16) (dual of [24, 5, 17]-code), using
- extended algebraic-geometric code AG_e(F,7P) [i] based on function field F/F₈ with g(F) = 3 and N(F) ≥ 24, using
  - the Klein quartic over F₈ [i]
linear OOA(2³, 3, F₂, 2, 3) (dual of [(3, 2), 3, 4]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(2;3,2) [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(2¹²⁹, 72, F₂, 2, 66) (dual of [(72, 2), 15, 67]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(2¹²⁹, 72, F₂, 2, 65) (dual of [(72, 2), 15, 66]-NRT-code)	[i]		Strength Reduction for OOAs
3	Linear OOA(2¹²⁸, 71, F₂, 2, 66) (dual of [(71, 2), 14, 67]-NRT-code)	[i]		Truncation for OOAs
4	Linear OOA(2¹²⁷, 71, F₂, 2, 65) (dual of [(71, 2), 15, 66]-NRT-code)	[i]
5	Linear OOA(2¹²⁵, 70, F₂, 2, 63) (dual of [(70, 2), 15, 64]-NRT-code)	[i]
6	Linear OOA(2¹²⁹, 36, F₂, 4, 67) (dual of [(36, 4), 15, 68]-NRT-code)	[i]		OOA Folding