MinT - Information on Result #2225880

Information on Result #2225880

Linear OA(2²¹¹, 263, F₂, 74) (dual of [263, 52, 75]-code), using 1 times truncation based on linear OA(2²¹², 264, F₂, 75) (dual of [264, 52, 76]-code), using

concatenation of two codes [i] based on
1. linear OA(16²⁰, 33, F₁₆, 18) (dual of [33, 13, 19]-code), using
  - extended algebraic-geometric code AG_e(F,14P) [i] based on function field F/F₁₆ with g(F) = 2 and N(F) ≥ 33, using
    - a function field by SÃ©mirat [i]
2. linear OA(2⁴, 8, F₂, 3) (dual of [8, 4, 4]-code or 8-cap in PG(3,2)), using
  - Reedâ€“Muller code RM(1,3) [i]
  - caps in base bÂ =Â 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 OA(2²¹³, 265, F₂, 74) (dual of [265, 52, 75]-code)	[i]		Code Embedding in Larger Space
2	Linear OA(2²¹⁴, 266, F₂, 74) (dual of [266, 52, 75]-code)	[i]
3	Linear OA(2²¹⁵, 267, F₂, 74) (dual of [267, 52, 75]-code)	[i]
4	Linear OA(2²¹⁶, 268, F₂, 74) (dual of [268, 52, 75]-code)	[i]
5	Linear OA(2²¹⁷, 269, F₂, 74) (dual of [269, 52, 75]-code)	[i]
6	Linear OA(2²¹⁸, 270, F₂, 74) (dual of [270, 52, 75]-code)	[i]
7	Linear OA(2²¹⁹, 271, F₂, 74) (dual of [271, 52, 75]-code)	[i]
8	Linear OA(2²²⁰, 272, F₂, 74) (dual of [272, 52, 75]-code)	[i]
9	Linear OA(2²²¹, 273, F₂, 74) (dual of [273, 52, 75]-code)	[i]
10	Linear OA(2²²², 274, F₂, 74) (dual of [274, 52, 75]-code)	[i]
11	Linear OA(2²¹⁸, 271, F₂, 74) (dual of [271, 53, 75]-code)	[i]		ConstructionÂ X with VarÅ¡amov Bound
12	Linear OA(2²²², 276, F₂, 74) (dual of [276, 54, 75]-code)	[i]		ConstructionÂ X with VarÅ¡amov Bound
13	Linear OOA(2²¹¹, 131, F₂, 2, 74) (dual of [(131, 2), 51, 75]-NRT-code)	[i]		OOA Folding
14	Linear OOA(2²¹¹, 87, F₂, 3, 74) (dual of [(87, 3), 50, 75]-NRT-code)	[i]		OOA Folding