MinT - Information on Result #661495

Information on Result #661495

Linear OA(2²⁵¹, 396, F₂, 67) (dual of [396, 145, 68]-code), using concatenation of two codes based on

linear OA(32³⁷, 66, F₃₂, 33) (dual of [66, 29, 34]-code), using
- constructionÂ X applied to AG(F,29P) âŠ‚ AG(F,31P) [i] based on
  1. linear OA(32³⁶, 63, F₃₂, 33) (dual of [63, 27, 34]-code), using algebraic-geometric code AG(F,29P) [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(32³⁴, 63, F₃₂, 31) (dual of [63, 29, 32]-code), using algebraic-geometric code AG(F,31P) [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(2²⁵¹, 396, F₂, 66) (dual of [396, 145, 67]-code)	[i]	Strength Reduction
2	Linear OA(2²⁵², 397, F₂, 67) (dual of [397, 145, 68]-code)	[i]	Code Embedding in Larger Space
3	Linear OA(2²⁵³, 398, F₂, 67) (dual of [398, 145, 68]-code)	[i]
4	Linear OA(2²⁵⁴, 399, F₂, 67) (dual of [399, 145, 68]-code)	[i]
5	Linear OA(2²⁵⁵, 400, F₂, 67) (dual of [400, 145, 68]-code)	[i]
6	Linear OA(2²⁵⁰, 395, F₂, 66) (dual of [395, 145, 67]-code)	[i]	Truncation
7	Linear OOA(2²⁵¹, 198, F₂, 2, 67) (dual of [(198, 2), 145, 68]-NRT-code)	[i]	OOA Folding
8	Linear OOA(2²⁵¹, 132, F₂, 3, 67) (dual of [(132, 3), 145, 68]-NRT-code)	[i]	OOA Folding