MinT - Information on Result #2225883

Information on Result #2225883

Linear OA(2²⁰⁷, 263, F₂, 70) (dual of [263, 56, 71]-code), using 1 times truncation based on linear OA(2²⁰⁸, 264, F₂, 71) (dual of [264, 56, 72]-code), using

concatenation of two codes [i] based on
1. linear OA(16¹⁹, 33, F₁₆, 17) (dual of [33, 14, 18]-code), using
  - extended algebraic-geometric code AG_e(F,15P) [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(2²⁰⁹, 265, F₂, 70) (dual of [265, 56, 71]-code)	[i]		Code Embedding in Larger Space
2	Linear OA(2²¹⁰, 266, F₂, 70) (dual of [266, 56, 71]-code)	[i]
3	Linear OA(2²¹¹, 267, F₂, 70) (dual of [267, 56, 71]-code)	[i]
4	Linear OA(2²¹², 268, F₂, 70) (dual of [268, 56, 71]-code)	[i]
5	Linear OA(2²¹³, 269, F₂, 70) (dual of [269, 56, 71]-code)	[i]
6	Linear OA(2²¹⁴, 270, F₂, 70) (dual of [270, 56, 71]-code)	[i]
7	Linear OA(2²¹⁵, 271, F₂, 70) (dual of [271, 56, 71]-code)	[i]
8	Linear OA(2²¹⁶, 272, F₂, 70) (dual of [272, 56, 71]-code)	[i]
9	Linear OA(2²¹⁷, 273, F₂, 70) (dual of [273, 56, 71]-code)	[i]
10	Linear OA(2²¹⁵, 273, F₂, 70) (dual of [273, 58, 71]-code)	[i]		VarÅ¡amovâ€“Edel Lengthening
11	Linear OA(2²¹⁷, 276, F₂, 70) (dual of [276, 59, 71]-code)	[i]		VarÅ¡amovâ€“Edel Lengthening
12	Linear OA(2²¹², 269, F₂, 70) (dual of [269, 57, 71]-code)	[i]		ConstructionÂ X with VarÅ¡amov Bound
13	Linear OA(2²¹⁶, 274, F₂, 70) (dual of [274, 58, 71]-code)	[i]
14	Linear OA(2²¹⁸, 277, F₂, 70) (dual of [277, 59, 71]-code)	[i]
15	Linear OOA(2²⁰⁷, 131, F₂, 2, 70) (dual of [(131, 2), 55, 71]-NRT-code)	[i]		OOA Folding
16	Linear OOA(2²⁰⁷, 87, F₂, 3, 70) (dual of [(87, 3), 54, 71]-NRT-code)	[i]		OOA Folding