MinT - Information on Result #1461827

Information on Result #1461827

Linear OOA(32¹⁰⁶, 19408, F₃₂, 2, 36) (dual of [(19408, 2), 38710, 37]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(32¹⁰⁶, 19408, F₃₂, 36) (dual of [19408, 19302, 37]-code), using

discarding factors / shortening the dual code based on linear OA(32¹⁰⁶, 32780, F₃₂, 36) (dual of [32780, 32674, 37]-code), using
- 1 times code embedding in larger space [i] based on linear OA(32¹⁰⁵, 32779, F₃₂, 36) (dual of [32779, 32674, 37]-code), using
  - constructionÂ X applied to C_e(35) âŠ‚ C_e(32) [i] based on
    1. linear OA(32¹⁰³, 32768, F₃₂, 36) (dual of [32768, 32665, 37]-code), using an extension C_e(35) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 32³âˆ’1, defining interval IÂ =Â [1,35], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 36 [i]
    2. linear OA(32⁹⁴, 32768, F₃₂, 33) (dual of [32768, 32674, 34]-code), using an extension C_e(32) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 32³âˆ’1, defining interval IÂ =Â [1,32], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 33 [i]
    3. linear OA(32², 11, F₃₂, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,32)), using
      - discarding factors / shortening the dual code based on linear OA(32², 32, F₃₂, 2) (dual of [32, 30, 3]-code or 32-arc in PG(1,32)), using
        Reedâ€“Solomon code RS(30,32) [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(32¹⁰⁶, 2156, F₃₂, 38, 36) (dual of [(2156, 38), 81822, 37]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row