On self-dual codes over some prime fields
نویسندگان
چکیده
In this paper, we study self-dual codes over GF(p) where p = 11, 13, 17, 19, 23 and 29. A classification of such codes for small lengths is given. The largest minimum weights of these codes are investigated. Many maximum distance separable self-dual codes are constructed.
منابع مشابه
Construction of MDS self-dual codes from orthogonal matrices
In this paper, we give algorithms and methods of construction of self-dual codes over finite fields using orthogonal matrices. Randomization in the orthogonal group, and code extension are the main tools. Some optimal, almost MDS, and MDS self-dual codes over both small and large prime fields are constructed.
متن کاملOn the decomposition of self-dual codes over F2+uF2 with an automorphism of odd prime order
We present a general theory of decomposing self-dual codes over F2 +uF2 that have an automorphism of odd prime order. Using this decomposition we classify all Lee-extremal/optimal self-dual codes of lengths 9 to 16 with an odd order automorphism and partially classify those of lengths 17 to 20. In particular we find 945 inequivalent Lee-extremal self-dual codes of length 20. © 2006 Elsevier Inc...
متن کاملSelf-dual codes over F2 + uF2 with an automorphism of odd order
We complete the classification of all Lee-extremal and Lee-optimal self-dual codes over F2 + uF2 of lengths 9 through 20 that have a nontrivial odd order automorphism begun in [W.C. Huffman, On the decomposition of self-dual codes over F2 + uF2 with an automorphism of odd prime order, Finite Fields Appl., in press]. Along the way, we find all Lee-extremal self-dual codes over F2 + uF2 of length...
متن کاملRepeated-Root Self-Dual Negacyclic Codes over Finite Fields
Let Fq be a finite field with q = p , where p is an odd prime. In this paper, we study the repeated-root self-dual negacyclic codes over Fq. The enumeration of such codes is investigated. We obtain all the self-dual negacyclic codes of length 2p over Fq, a ≥ 1. The construction of self-dual negacyclic codes of length 2bp over Fq is also provided, where gcd(2, b) = gcd(b, p) = 1 and a ≥ 1.
متن کاملClassification of binary self-dual [48, 24, 10] codes with an automorphism of odd prime order
The purpose of this paper is to complete the classification of binary self-dual [48, 24, 10] codes with an automorphism of odd prime order. We prove that if there is a self-dual [48, 24, 10] code with an automorphism of type p-(c, f) with p being an odd prime, then p = 3, c = 16, f = 0. By considering only an automorphism of type 3-(16, 0), we prove that there are exactly 264 inequivalent self-...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Discrete Mathematics
دوره 262 شماره
صفحات -
تاریخ انتشار 2003