SHORTEST LCD EMBEDDINGS OF BINARY, TERNARY AND QUATERNARY LINEAR CODES

초록

In recent years, there has been active research on selforthogonal embeddings of linear codes since they have yielded some optimal selforthogonal codes. LCD codes have a trivial hull, so they are counterparts of selforthogonal codes. It is therefore a natural question whether one can embed linear codes into distanceoptimal LCD codes. To answer this, we first determine the num ber of columns to be added to a generator matrix of a linear code in order to embed the given code into an LCD code. Then, we characterize all possible forms of the shortest LCD embeddings of a linear code. Using the shortest LCD embedding method, we find new ternary LCD codes with parameters includ ing [23, 4, 14], [23, 5, 12], [24, 6, 12], and [25, 5, 14] and a new quaternary LCD [21, 10, 8] code, each of which has minimum distance one greater than those of the known codes. This shows that our shortest LCD embedding method is useful in finding distanceoptimal LCD codes over various fields. © 2026 American Institute of Mathematical Sciences. All rights reserved.

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