MinT - Information on Result #2226796

Information on Result #2226796

Linear OA(2²⁴⁵, 395, F₂, 64) (dual of [395, 150, 65]-code), using 1 times truncation based on linear OA(2²⁴⁶, 396, F₂, 65) (dual of [396, 150, 66]-code), using

concatenation of two codes [i] based on
1. 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]
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(2²⁴⁷, 397, F₂, 64) (dual of [397, 150, 65]-code)	[i]	Code Embedding in Larger Space
2	Linear OOA(2²⁴⁵, 197, F₂, 2, 64) (dual of [(197, 2), 149, 65]-NRT-code)	[i]	OOA Folding
3	Linear OOA(2²⁴⁵, 131, F₂, 3, 64) (dual of [(131, 3), 148, 65]-NRT-code)	[i]	OOA Folding