MinT - Information on Result #1641864

Information on Result #1641864

Linear OOA(3⁹⁰, 1682608, F₃, 5, 10) (dual of [(1682608, 5), 8412950, 11]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3⁹⁰, 1682608, F₃, 2, 10) (dual of [(1682608, 2), 3365126, 11]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3⁹⁰, 2391501, F₃, 2, 10) (dual of [(2391501, 2), 4782912, 11]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3⁹⁰, 4783002, F₃, 10) (dual of [4783002, 4782912, 11]-code), using
  - 1 times code embedding in larger space [i] based on linear OA(3⁸⁹, 4783001, F₃, 10) (dual of [4783001, 4782912, 11]-code), using
    - constructionÂ X applied to C_e(9) âŠ‚ C_e(6) [i] based on
      1. linear OA(3⁸⁵, 4782969, F₃, 10) (dual of [4782969, 4782884, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 3¹⁴âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
      2. linear OA(3⁵⁷, 4782969, F₃, 7) (dual of [4782969, 4782912, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 3¹⁴âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
      3. linear OA(3⁴, 32, F₃, 2) (dual of [32, 28, 3]-code), using
        discarding factors / shortening the dual code based on linear OA(3⁴, 40, F₃, 2) (dual of [40, 36, 3]-code), using
        Hamming code H(4,3) [i]

Mode: Linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m 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(3⁹⁰, 1682607, F₃, 15, 10) (dual of [(1682607, 15), 25239015, 11]-NRT-code)	[i]		OOA Stacking with Additional Row