MinT - Information on Result #2238658

Information on Result #2238658

Linear OA(4⁷³, 4102, F₄, 16) (dual of [4102, 4029, 17]-code), using 1 times truncation based on linear OA(4⁷⁴, 4103, F₄, 17) (dual of [4103, 4029, 18]-code), using

constructionÂ X applied to C_e(16) âŠ‚ C_e(14) [i] based on
1. linear OA(4⁷³, 4096, F₄, 17) (dual of [4096, 4023, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 4⁶âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
2. linear OA(4⁶⁷, 4096, F₄, 15) (dual of [4096, 4029, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 4⁶âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
3. linear OA(4¹, 7, F₄, 1) (dual of [7, 6, 2]-code), using
  - discarding factors / shortening the dual code based on linear OA(4¹, s, F₄, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
    - parity-check code [i]

Mode: Constructive and 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		Method
1	Linear OOA(4⁷³, 2505, F₄, 2, 16) (dual of [(2505, 2), 4937, 17]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(4⁷³, 2505, F₄, 3, 16) (dual of [(2505, 3), 7442, 17]-NRT-code)	[i]
3	Digital (57, 73, 2505)-net over F₄	[i]
4	Linear OA(4⁷⁸, 4131, F₄, 16) (dual of [4131, 4053, 17]-code)	[i]	VarÅ¡amovâ€“Edel Lengthening
5	Linear OA(4⁷⁹, 4159, F₄, 16) (dual of [4159, 4080, 17]-code)	[i]
6	Linear OA(4⁸⁰, 4213, F₄, 16) (dual of [4213, 4133, 17]-code)	[i]
7	Linear OA(4⁸¹, 4312, F₄, 16) (dual of [4312, 4231, 17]-code)	[i]
8	Linear OOA(4⁷³, 2051, F₄, 2, 16) (dual of [(2051, 2), 4029, 17]-NRT-code)	[i]	OOA Folding
9	Linear OOA(4⁷³, 1367, F₄, 3, 16) (dual of [(1367, 3), 4028, 17]-NRT-code)	[i]	OOA Folding