MinT - Information on Result #1439354

Information on Result #1439354

Linear OOA(5¹²⁸, 56964, F₅, 2, 22) (dual of [(56964, 2), 113800, 23]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(5¹²⁸, 56964, F₅, 22) (dual of [56964, 56836, 23]-code), using

discarding factors / shortening the dual code based on linear OA(5¹²⁸, 78161, F₅, 22) (dual of [78161, 78033, 23]-code), using
- constructionÂ X applied to C_e(21) âŠ‚ C_e(16) [i] based on
  1. linear OA(5¹²⁰, 78125, F₅, 22) (dual of [78125, 78005, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 78124Â = 5⁷âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
  2. linear OA(5⁹², 78125, F₅, 17) (dual of [78125, 78033, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 78124Â = 5⁷âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [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(5¹²⁸, 28482, F₅, 3, 22) (dual of [(28482, 3), 85318, 23]-NRT-code)	[i]		OOA Folding