MinT - Information on Result #1060488

Information on Result #1060488

Linear OOA(3²⁴⁰, 2391509, F₃, 4, 18) (dual of [(2391509, 4), 9565796, 19]-NRT-code), using OOA 2-folding based on linear OOA(3²⁴⁰, 4783018, F₃, 2, 18) (dual of [(4783018, 2), 9565796, 19]-NRT-code), using

trace code [i] based on linear OOA(9¹²⁰, 2391509, F₉, 2, 18) (dual of [(2391509, 2), 4782898, 19]-NRT-code), using
- OOA 2-folding [i] based on linear OA(9¹²⁰, 4783018, F₉, 18) (dual of [4783018, 4782898, 19]-code), using
  - constructionÂ X applied to C_e(18) âŠ‚ C_e(11) [i] based on
    1. linear OA(9¹¹³, 4782969, F₉, 19) (dual of [4782969, 4782856, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
    2. linear OA(9⁷¹, 4782969, F₉, 12) (dual of [4782969, 4782898, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
    3. linear OA(9⁷, 49, F₉, 5) (dual of [49, 42, 6]-code), using
      - discarding factors / shortening the dual code based on linear OA(9⁷, 73, F₉, 5) (dual of [73, 66, 6]-code), using
        a code by Danev and Olsson [i]

Mode: Constructive and 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(3²⁴¹, 2391509, F₃, 4, 18) (dual of [(2391509, 4), 9565795, 19]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(3²⁴², 2391509, F₃, 4, 18) (dual of [(2391509, 4), 9565794, 19]-NRT-code)	[i]		OOA Duplication