MinT - Information on Result #2429373

Information on Result #2429373

Linear OOA(2²⁵⁶, 136, F₂, 2, 135) (dual of [(136, 2), 16, 136]-NRT-code), using strength reduction based on linear OOA(2²⁵⁶, 136, F₂, 2, 139) (dual of [(136, 2), 16, 140]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(16¹³, 17, F₁₆, 13) (dual of [17, 4, 14]-code or 17-arc in PG(12,16)), using
  - extended Reedâ€“Solomon code RS_e(4,16) [i]
  - the expurgated narrow-sense BCH-code C(I) with length 17Â | 16²âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]
2. linear OOA(2¹², 8, F₂, 2, 9) (dual of [(8, 2), 4, 10]-NRT-code), using
  - an explicit generator matrix by Edel [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(2²⁵⁷, 136, F₂, 2, 135) (dual of [(136, 2), 15, 136]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2²⁵⁴, 135, F₂, 2, 133) (dual of [(135, 2), 16, 134]-NRT-code)	[i]	Truncation for OOAs
3	Linear OOA(2²⁵³, 134, F₂, 2, 132) (dual of [(134, 2), 15, 133]-NRT-code)	[i]
4	Linear OOA(2²⁵², 134, F₂, 2, 131) (dual of [(134, 2), 16, 132]-NRT-code)	[i]
5	Linear OOA(2²⁵¹, 133, F₂, 2, 130) (dual of [(133, 2), 15, 131]-NRT-code)	[i]
6	Linear OOA(2²⁵⁰, 133, F₂, 2, 129) (dual of [(133, 2), 16, 130]-NRT-code)	[i]
7	Linear OOA(2²⁴⁹, 132, F₂, 2, 128) (dual of [(132, 2), 15, 129]-NRT-code)	[i]
8	Linear OOA(2²⁴⁸, 132, F₂, 2, 127) (dual of [(132, 2), 16, 128]-NRT-code)	[i]
9	Linear OOA(2²⁴⁷, 131, F₂, 2, 126) (dual of [(131, 2), 15, 127]-NRT-code)	[i]
10	Linear OOA(2²⁴⁶, 131, F₂, 2, 125) (dual of [(131, 2), 16, 126]-NRT-code)	[i]
11	Linear OOA(2²⁴⁵, 130, F₂, 2, 124) (dual of [(130, 2), 15, 125]-NRT-code)	[i]
12	Linear OOA(2²⁴³, 129, F₂, 2, 122) (dual of [(129, 2), 15, 123]-NRT-code)	[i]
13	Linear OOA(2²⁴², 129, F₂, 2, 121) (dual of [(129, 2), 16, 122]-NRT-code)	[i]
14	Linear OOA(2²⁴¹, 128, F₂, 2, 120) (dual of [(128, 2), 15, 121]-NRT-code)	[i]