MinT - Information on Result #1439996

Information on Result #1439996

Linear OOA(5¹⁴⁰, 14371, F₅, 2, 28) (dual of [(14371, 2), 28602, 29]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(5¹⁴⁰, 14371, F₅, 28) (dual of [14371, 14231, 29]-code), using

discarding factors / shortening the dual code based on linear OA(5¹⁴⁰, 15651, F₅, 28) (dual of [15651, 15511, 29]-code), using
- constructionÂ X applied to C_e(27) âŠ‚ C_e(22) [i] based on
  1. linear OA(5¹³³, 15625, F₅, 28) (dual of [15625, 15492, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 5⁶âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
  2. linear OA(5¹⁰⁹, 15625, F₅, 23) (dual of [15625, 15516, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 5⁶âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
  3. linear OA(5⁷, 26, F₅, 4) (dual of [26, 19, 5]-code), using
    - base reduction for projective spaces (embedding PG(3,25) in PG(6,5)) [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(5¹⁴⁰, 7185, F₅, 3, 28) (dual of [(7185, 3), 21415, 29]-NRT-code)	[i]		OOA Folding