Luo, 51, was taken from the Liaoning carrier and was pronounced dead at a hospital, a report by the state-owned news agency Xinhua said.
Luo was chairman and general manager of the Shenyang Aircraft Corp.
Flags were flown at half-staff at the gates of the factory in Shenyang, capital of northeast China's Liaoning province.
Xinhua reported that electronic screens at the factory gates read "Mourn General Manager Luo Yang. Luo will be immortal."
SAC is a subsidiary of China's state-owned aircraft maker, the Aviation Industry Corp. of China.
The J-15 is China's first generation multipurpose, carrier-borne fighter and the landing and takeoff exercises aboard the Liaoning carrier were the first for the vessel, which was commissioned in September.
The aircraft can carry anti-ship, air-to-air and air-to-ground missiles, as well as precision-guided bombs and is comparable in performance to the Russian Sukhoi Su-33 and the McDonnell Douglas -- now Boeing -- F/A-18 Hornet, Xinhua said.
A report by GlobalSecurity.org said the J-15 -- dubbed the Flying Shark -- is said to be a reverse-engineered aircraft based on an unfinished Su-33 prototype bought from Ukraine around 2001.
Chinese media criticized Western media for creating doubt that the J-15 was anything but home-grown technology, saying assertions of reverse engineering are "groundless and sour."
Xinhua reported that the criticism wasn't surprising since the J-15 has a similar aerodynamic shape to that of the Russian Su-33.
The Xinhua commentary said China is always heavily criticized for alleged plagiarism "when the country makes progress in military hardware development, questioning China's respect to others' intellectual property rights and belittling the hardware's technological and tactical qualities."
The report said "it is true that China used to rely heavily on imported Russian military aircraft, warships and other hardware to modernize its troops due to a lack of independent innovation abilities."
But China has made breakthroughs in manufacturing turbofan engines, which provide high-performance, home-made fighter jets, the Xinhua report said.
Chinese officials have said the combination of J-15 aircraft and the Liaoning aircraft carrier will make it easier for China to protect maritime interests.
China is disputing several island groupings in the South China Sea with neighboring countries including Japan, Vietnam, Taiwan and the Philippines.
Tensions have increased in the past year because of Chinese fishing ships and patrol vessels sailing into what other countries regard as their territorial waters around the disputed islands, many of which are controlled by countries other than China.