South Korea has launched a concerted campaign that it hopes will lead to trade and eventual establishment of full diplomatic relations with China, its Communist enemy for the past three decades.

In a series of speeches and public statements, Sough Korean officials are signaling the Chinese that they are eager to explore trade and cultural arrangements and to discuss ways of easing tension on the Korean peninsula.

So far, their signals have not been answered, at least not publicly, and they assume that Peking is not yet willing to risk arousing the wrath of North Korea in order to make deals with the South.

But the Seoul gevernment, oozing confidence over its enduring economic progress, believes that eventually China will respond.

"A change will take place in due course," said one senior government official. "I cannot envisage this state of having no relations will last forever. Something has got to happen.

"We are enough of a substance as a country now that eventually China -- and Russia, too -- will realize it is nonsense not to deal with us."

The opening toward Peking is not entirely new. More than five years ago, President Park Chung Hee changed his country's foreign policy fundamentally by declaring a willingness to have diplomatic relations with any country regardless of ideological differences.

But the campaign began in earnest this winter as it became clear that the United States, South Korea's ally and protector for 30 years, would normalize relations with the government that both countries fought in the early 1950s.

Kim Kyung Won, who is Park's chief foreign affairs adviser, told the press in Hong Kong in late October that his country is prepared to establish diplomatic relations with China and that ideological differences should not stand intheway. The message has been repeated several times in press briegings since then and the foreign minister, Park Tong Jin, has pointedly assured businessmen here that the government will encourage them to seek trade contacts with the Chinese.

The South Koreans have privately sketched out a general diplomatic plan. First a series of non-political exchanges, or "confidence-builders" as they are called here would be attempted. These would include cultural exchanges, sports contests like the recently completed Asian Games in Bangkok where South Korean and Chinese players competed, and ultimately trade.

Economists in Seoul are researching the trade field to determine the most likely prospects for two-way buying and selling. They believe China can sell South Korea coal and coke and possibly oil, although the type of oil China might export is not the kind South Korea can use without extensive technological changes.

In Xchange, the economists here think China is a big potential market for both consumer goods and manufactured products. Of course the rest of the world is lining up to sell China tht same goods, but South Korean industries could have a substantial price advantage over both Japanese and American suppliers. In addition, it is considered likely that the Chinese could use precisely the type of basis, low-level technology for modernization that South Korea has used in the past 10 years to launch its own industrial development so successfully.

"We have no direct channels open to tell the Chinese all this," said one official, "but they already know. We have been loud enough in our public statements and they are rational enough to know what we mean."

He emphasized that political differences are no obstacle from South Korea's point of view. "We wuould be delighted to take the same posture as the Japanese and separate politics from economics," the official added with a laugh.

The United States has recently indicated a definite interest in assisting South Korea to improve its relations with both China and the Soviet Uniton. Answering reporters' questions here recently, U.S. Amabassador William Gleysteen said, "We certainly would be prepared to play a role of middleman if that is desirable." There are no "secret contacts" under way that the Seoul government is not aware of, he added.

There has been much speculation that the United States' new diplomatic relations with Peking may serve ultiations between North and South Korea, aimed at reunification of the two countries which have been divided since the early 1950s.

It is known here that the United States and China already have discussed the Korean problem at some level but if any progress has been made no one is revealing it.

"We are aware that the U.S. and China have included Korea within their conversations, but we think that it is not a major part of their agenda," said the senior government official.

In recent months, North Korea has lined up more closely with China than with the Soviet Union, although it attempts to preserve good relations with both Communist neighbors.

South Korean officials doubt, however, that China has as much influence on North Korea as most Western analysts have believed. In the continuing confrontation along the Soviet border, China does not want to do anything that might alienate North Korea and will definitely not push that country into negotiations it does not want, the official said.