MinT - Information on Result #2226753

Information on Result #2226753

Linear OA(2²⁴³, 383, F₂, 66) (dual of [383, 140, 67]-code), using 1 times truncation based on linear OA(2²⁴⁴, 384, F₂, 67) (dual of [384, 140, 68]-code), using

concatenation of two codes [i] based on
1. linear OA(32³⁶, 64, F₃₂, 33) (dual of [64, 28, 34]-code), using
  - extended algebraic-geometric code AG_e(F,30P) [i] based on function field F/F₃₂ with g(F) = 3 and N(F) ≥ 64, using
    - a function field by SÃ©mirat [i]
2. linear OA(2¹, 6, F₂, 1) (dual of [6, 5, 2]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
    - parity-check code [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 OA(2²⁴⁵, 385, F₂, 66) (dual of [385, 140, 67]-code)	[i]	Code Embedding in Larger Space
2	Linear OA(2²⁴⁶, 386, F₂, 66) (dual of [386, 140, 67]-code)	[i]
3	Linear OA(2²⁴⁷, 387, F₂, 66) (dual of [387, 140, 67]-code)	[i]
4	Linear OA(2²⁴⁸, 388, F₂, 66) (dual of [388, 140, 67]-code)	[i]
5	Linear OA(2²⁴⁹, 389, F₂, 66) (dual of [389, 140, 67]-code)	[i]
6	Linear OA(2²⁵⁰, 396, F₂, 66) (dual of [396, 146, 67]-code)	[i]	VarÅ¡amovâ€“Edel Lengthening
7	Linear OA(2²⁴⁶, 387, F₂, 66) (dual of [387, 141, 67]-code)	[i]	ConstructionÂ X with VarÅ¡amov Bound
8	Linear OA(2²⁴⁸, 390, F₂, 66) (dual of [390, 142, 67]-code)	[i]
9	Linear OA(2²⁴⁹, 392, F₂, 66) (dual of [392, 143, 67]-code)	[i]
10	Linear OOA(2²⁴³, 191, F₂, 2, 66) (dual of [(191, 2), 139, 67]-NRT-code)	[i]	OOA Folding
11	Linear OOA(2²⁴³, 127, F₂, 3, 66) (dual of [(127, 3), 138, 67]-NRT-code)	[i]	OOA Folding