MinT - Information on Result #1550434

Information on Result #1550434

Linear OOA(5¹³⁷, 199655, F₅, 3, 21) (dual of [(199655, 3), 598828, 22]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(5¹³⁷, 199655, F₅, 21) (dual of [199655, 199518, 22]-code), using

discarding factors / shortening the dual code based on linear OA(5¹³⁷, 390665, F₅, 21) (dual of [390665, 390528, 22]-code), using
- constructionÂ X applied to C_e(20) âŠ‚ C_e(15) [i] based on
  1. linear OA(5¹²⁹, 390625, F₅, 21) (dual of [390625, 390496, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 5⁸âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
  2. linear OA(5⁹⁷, 390625, F₅, 16) (dual of [390625, 390528, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 5⁸âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
  3. linear OA(5⁸, 40, F₅, 4) (dual of [40, 32, 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(5¹³⁷, 49913, F₅, 27, 21) (dual of [(49913, 27), 1347514, 22]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row