ECE full form is Electronics and communication engineering. After doing ECE it's not neccessary to go into core company. You can get any Job after doing ECE. The core companies are-

1. Wipro Lighting Corporate
2. Schnider Electric
3. Bajaj Electricals Ltd
4. Siemens
5. Alstom Corporate
6. Bharat Heavy Electrical Ltd.
7. Crompton Greaves
8. Havells India Limited
9. ABB India Limited
10. EMCO limited
11. HBM power system
12. KIRLOSKAR Electric Company Limited
13. Ace Bimetalliks India Pvt. Ltd.
14. Balar Marketing Pvt. Ltd
15. E S Electronics (India) Pvt. Ltd
16. Modern Electrical Stores
17. Eveready Industries India Ltd
18. Microtek
19. Exide Industries Ltd
20. Ankit Electricals
21. Arihant Enterprises
22. Advance Engineering Company
23. Jindal Steel & Power Ltd.
24. Tata Electric Companies
25. Techno Instrument India Pvt.Ltd
26. Adani Power Ltd
27. CESC Ltd.
28. Jaiprakash Power Ventures Ltd
29. PTC India Ltd
30. Sun Source (India)
31. Kaydour Cables India
32. Finolex Cables Limited
33. Impex Trading Company
34. Sevana Electrical Group
35. Dynamic Scaffolding & Equipment Co
36. Neolex Cables
37. National Wind & Power Corpn.
38. Gujarat Industries Power Company Ltd
39. HBL Power Systems Ltd
40. Suryachakra Power Corpn. Ltd
41. DLF Power Limited
42. Lanco Industries
43. Kuber Lighting Pvt Ltd
44. Baliga Lighting
45. A.K. Electricals
46. Torque Master Tools Pvt. Ltd
47. Pran Electronics Pvt. Ltd.
48. Mellcon Engineers
49. Mehta Engineering Enterprise
50. India International House Ltd.

The above core companies are based on India only.