Perfect codes in poset block spaces. (English) Zbl 1402.94081
Summary: There is a limited class of perfect codes with respect to the classical Hamming metric. There are other kind of metrics with respect to which perfect codes have been investigated viz. poset metric, block metric and poset block metric. Given the minimal elements of a poset, a necessary and sufficient condition for 1-perfectness of a poset block code has been derived. A necessary and sufficient condition for a poset block code to be \(r\)-perfect has also been considered. Further, for each \(r\), \(1\leq r\leq n-k\), a sufficient condition that ensures the existence of a poset block structure which turns a given code into an \(r\)-perfect poset block code has been obtained. Several illustrations of well known codes to be \(r\)-perfect for specific values of \(r\) have been explored.
MSC:
| 94B05 | Linear codes (general theory) |
| 94B25 | Combinatorial codes |
| 94B60 | Other types of codes |
| 94B65 | Bounds on codes |
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