MinT - Information on Result #1522151

Information on Result #1522151

Linear OOA(3¹⁰⁷, 87958, F₃, 3, 14) (dual of [(87958, 3), 263767, 15]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁰⁷, 87958, F₃, 2, 14) (dual of [(87958, 2), 175809, 15]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁰⁷, 88593, F₃, 2, 14) (dual of [(88593, 2), 177079, 15]-NRT-code), using
- 3¹ times duplication [i] based on linear OOA(3¹⁰⁶, 88593, F₃, 2, 14) (dual of [(88593, 2), 177080, 15]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3¹⁰⁶, 177186, F₃, 14) (dual of [177186, 177080, 15]-code), using
    - constructionÂ X applied to C_e(13) âŠ‚ C_e(9) [i] based on
      1. linear OA(3¹⁰⁰, 177147, F₃, 14) (dual of [177147, 177047, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
      2. linear OA(3⁶⁷, 177147, F₃, 10) (dual of [177147, 177080, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
      3. linear OA(3⁶, 39, F₃, 3) (dual of [39, 33, 4]-code or 39-cap in PG(5,3)), using
        discarding factors / shortening the dual code based on linear OA(3⁶, 48, F₃, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
        large caps in PG(5,Â b) [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(3¹⁰⁷, 43979, F₃, 5, 14) (dual of [(43979, 5), 219788, 15]-NRT-code)	[i]		OOA Folding