MinT - Information on Result #911212

Information on Result #911212

Linear OOA(2¹²³, 72, F₂, 2, 59) (dual of [(72, 2), 21, 60]-NRT-code), using concatenation of two NRT-codes based on

linear OA(8¹⁷, 24, F₈, 14) (dual of [24, 7, 15]-code), using
- extended algebraic-geometric code AG_e(F,9P) [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(2¹²³, 72, F₂, 2, 58) (dual of [(72, 2), 21, 59]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(2¹²³, 72, F₂, 2, 57) (dual of [(72, 2), 21, 58]-NRT-code)	[i]		Strength Reduction for OOAs
3	Linear OOA(2¹²⁵, 73, F₂, 2, 59) (dual of [(73, 2), 21, 60]-NRT-code)	[i]		NRT-Code Embedding in Larger Space
4	Linear OOA(2¹²², 71, F₂, 2, 58) (dual of [(71, 2), 20, 59]-NRT-code)	[i]		Truncation for OOAs
5	Linear OOA(2¹²¹, 71, F₂, 2, 57) (dual of [(71, 2), 21, 58]-NRT-code)	[i]
6	Linear OOA(2¹¹⁹, 70, F₂, 2, 55) (dual of [(70, 2), 21, 56]-NRT-code)	[i]
7	Linear OOA(2¹¹⁸, 69, F₂, 2, 54) (dual of [(69, 2), 20, 55]-NRT-code)	[i]
8	Linear OOA(2¹²³, 36, F₂, 4, 59) (dual of [(36, 4), 21, 60]-NRT-code)	[i]		OOA Folding