MinT - Information on Result #661494

Information on Result #661494

Linear OA(2²⁴⁶, 396, F₂, 65) (dual of [396, 150, 66]-code), using concatenation of two codes based on

linear OA(32³⁶, 66, F₃₂, 32) (dual of [66, 30, 33]-code), using
- constructionÂ X applied to AG(F,30P) âŠ‚ AG(F,32P) [i] based on
  1. linear OA(32³⁵, 63, F₃₂, 32) (dual of [63, 28, 33]-code), using algebraic-geometric code AG(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(32³³, 63, F₃₂, 30) (dual of [63, 30, 31]-code), using algebraic-geometric code AG(F,32P) [i] based on function field F/F₃₂ with g(F) = 3 and N(F) ≥ 64 (see above)
  3. linear OA(32¹, 3, F₃₂, 1) (dual of [3, 2, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(32¹, s, F₃₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]
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.

None.

The following results depend on this result:

	Result		Method
1	Linear OA(2²⁴⁶, 396, F₂, 64) (dual of [396, 150, 65]-code)	[i]	Strength Reduction
2	Linear OA(2²⁴⁷, 397, F₂, 65) (dual of [397, 150, 66]-code)	[i]	Code Embedding in Larger Space
3	Linear OA(2²⁴⁸, 398, F₂, 65) (dual of [398, 150, 66]-code)	[i]	Code Embedding in Larger Space
4	Linear OA(2²⁴⁵, 395, F₂, 64) (dual of [395, 150, 65]-code)	[i]	Truncation
5	Linear OOA(2²⁴⁶, 198, F₂, 2, 65) (dual of [(198, 2), 150, 66]-NRT-code)	[i]	OOA Folding
6	Linear OOA(2²⁴⁶, 132, F₂, 3, 65) (dual of [(132, 3), 150, 66]-NRT-code)	[i]	OOA Folding