MinT - Information on Result #1457286

Information on Result #1457286

Linear OOA(25⁹⁷, 14912, F₂₅, 2, 32) (dual of [(14912, 2), 29727, 33]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(25⁹⁷, 14912, F₂₅, 32) (dual of [14912, 14815, 33]-code), using

discarding factors / shortening the dual code based on linear OA(25⁹⁷, 15649, F₂₅, 32) (dual of [15649, 15552, 33]-code), using
- 1 times code embedding in larger space [i] based on linear OA(25⁹⁶, 15648, F₂₅, 32) (dual of [15648, 15552, 33]-code), using
  - constructionÂ X applied to C_e(31) âŠ‚ C_e(25) [i] based on
    1. linear OA(25⁹¹, 15625, F₂₅, 32) (dual of [15625, 15534, 33]-code), using an extension C_e(31) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 25³âˆ’1, defining interval IÂ =Â [1,31], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 32 [i]
    2. linear OA(25⁷³, 15625, F₂₅, 26) (dual of [15625, 15552, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 25³âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
    3. linear OA(25⁵, 23, F₂₅, 5) (dual of [23, 18, 6]-code or 23-arc in PG(4,25)), using
      - discarding factors / shortening the dual code based on linear OA(25⁵, 25, F₂₅, 5) (dual of [25, 20, 6]-code or 25-arc in PG(4,25)), using
        Reedâ€“Solomon code RS(20,25) [i]

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(25⁹⁷, 1863, F₂₅, 34, 32) (dual of [(1863, 34), 63245, 33]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row