MinT - Information on Result #1440116

Information on Result #1440116

Linear OOA(5¹⁴², 68306, F₅, 2, 24) (dual of [(68306, 2), 136470, 25]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(5¹⁴², 68306, F₅, 24) (dual of [68306, 68164, 25]-code), using

discarding factors / shortening the dual code based on linear OA(5¹⁴², 78161, F₅, 24) (dual of [78161, 78019, 25]-code), using
- constructionÂ X applied to C_e(23) âŠ‚ C_e(18) [i] based on
  1. linear OA(5¹³⁴, 78125, F₅, 24) (dual of [78125, 77991, 25]-code), using an extension C_e(23) of the primitive narrow-sense BCH-code C(I) with length 78124Â = 5⁷âˆ’1, defining interval IÂ =Â [1,23], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 24 [i]
  2. linear OA(5¹⁰⁶, 78125, F₅, 19) (dual of [78125, 78019, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 78124Â = 5⁷âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
  3. linear OA(5⁸, 36, F₅, 4) (dual of [36, 28, 5]-code), using
    - discarding factors / shortening the dual code based on linear OA(5⁸, 52, F₅, 4) (dual of [52, 44, 5]-code), using
      - trace code [i] based on linear OA(25⁴, 26, F₂₅, 4) (dual of [26, 22, 5]-code or 26-arc in PG(3,25)), using
        extended Reedâ€“Solomon code RS_e(22,25) [i]
        algebraic-geometric code AG(F, Q+9P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26, using the rational function field F₂₅(x) [i]
        algebraic-geometric code AG(F,7P) with degPÂ =Â 3 [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26 (see above)

Mode: 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		This result only	Method
1	Linear OOA(5¹⁴², 34153, F₅, 3, 24) (dual of [(34153, 3), 102317, 25]-NRT-code)	[i]		OOA Folding