MinT - Information on Result #668443

Information on Result #668443

Linear OA(32⁹³, 1147, F₃₂, 34) (dual of [1147, 1054, 35]-code), using (u,Â u+v)-construction based on

linear OA(32²⁹, 122, F₃₂, 17) (dual of [122, 93, 18]-code), using
- constructionÂ X applied to AG(F,101P) âŠ‚ AG(F,103P) [i] based on
  1. linear OA(32²⁸, 119, F₃₂, 17) (dual of [119, 91, 18]-code), using algebraic-geometric code AG(F,101P) [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
    - a function field by SÃ©mirat [i]
  2. linear OA(32²⁶, 119, F₃₂, 15) (dual of [119, 93, 16]-code), using algebraic-geometric code AG(F,103P) [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120 (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(32⁶⁴, 1025, F₃₂, 34) (dual of [1025, 961, 35]-code), using
- the BCH-code C(I) with length 1025Â | 32⁴âˆ’1, defining interval IÂ =Â {1,32,63,…,1024}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 35 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(32⁹³, 573, F₃₂, 2, 34) (dual of [(573, 2), 1053, 35]-NRT-code)	[i]		OOA Folding