Construction of the Best Binary Cyclic Codes of Even Length
This paper gives a method of construction for binary cyclic codes of even length out of shorter ones of odd length. This construction enables us to establish the set of the minimal distances reached by even length codes, and for each of these distances, to determine the associated generator polynomial of lowest degree. Thanks to this result we construct the complete table of the best possible binary cyclic codes on each minimal distance up to the length 64, finishing off in that way the table of the binary cyclic codes of odd length compiled by CHEN and lying in . It can be noticed that VAN LINT found similar results but for only few specific values, see .
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