Error detection of irreducible cyclic codes on q-ary symmetric channel

Irreducible cyclic codes are well-known classes of block codes. These codes have wide range of applications specifically in deep space. Their weight distribution of Irreducible cyclic codes is known in only a few cases specifically they are known for binary cyclic codes. Previously, it has been shown that irreducible binary cyclic codes of even dimension and their duals are either proper or not good for error detection. In this correspondence it has been established that irreducible cyclic codes in number of cases are proper when transmitted over q-ary symmetric channel. The nonzero weights of the codes treated with in this paper vary between one and four.

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