MinT - Information on Result #1550332

Information on Result #1550332

Linear OOA(5¹³⁵, 1214363, F₅, 3, 18) (dual of [(1214363, 3), 3642954, 19]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(5¹³⁵, 1214363, F₅, 18) (dual of [1214363, 1214228, 19]-code), using

discarding factors / shortening the dual code based on linear OA(5¹³⁵, 1953169, F₅, 18) (dual of [1953169, 1953034, 19]-code), using
- constructionÂ X applied to C_e(17) âŠ‚ C_e(12) [i] based on
  1. linear OA(5¹²⁷, 1953125, F₅, 18) (dual of [1953125, 1952998, 19]-code), using an extension C_e(17) of the primitive narrow-sense BCH-code C(I) with length 1953124Â = 5⁹âˆ’1, defining interval IÂ =Â [1,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [i]
  2. linear OA(5⁹¹, 1953125, F₅, 13) (dual of [1953125, 1953034, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 1953124Â = 5⁹âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
  3. linear OA(5⁸, 44, F₅, 4) (dual of [44, 36, 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(5¹³⁵, 404787, F₅, 21, 18) (dual of [(404787, 21), 8500392, 19]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row