Classification of perfect linear codes with crown poset structure
نویسندگان
چکیده
Brualdi et al. introduced the concept of poset codes. In this paper, we consider the problem of classifying all perfect linear codes when the set of coordinate positions is endowed with crown poset structure. We derive a Ramanujan–Nagell type diophantine equation which is satis ed by parameters of perfect linear P-code. Solving this equation, we characterize parameters of one and two error correcting perfect linear P-codes. c © 2002 Elsevier Science B.V. All rights reserved.
منابع مشابه
On the nonexistence of triple-error-correcting perfect binary linear codes with a crown poset structure
Ahn et al. [Discrete Math. 268 (2003) 21–30] characterized completely the parameters of singleand error-correcting perfect linear codes with a crown poset structure by solving Ramanujan–Nagelltype Diophantine equation. In this paper, we give a shorter proof for the same result by analyzing a generator matrix of a perfect linear code. Furthermore, we combine our method with the Johnson bound in ...
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ورودعنوان ژورنال:
- Discrete Mathematics
دوره 268 شماره
صفحات -
تاریخ انتشار 2003