Self-Dual Codes over GF(4)
نویسندگان
چکیده
This paper studies codes V over GF(4) which have even weights and have the same weight distribution as the dual code FL. Some of the results are as follows. All such codes satisfy VL = 4. (If VI = V, V has a binary basis.) The number of such V's is determined, and those of length <14 are completely classified. The weight enumerator of % is characterized and an upper bound obtained on the minimum distance. Necessary and sufficient conditions are given for %' to be extended cyclic. Two new 5-designs are constructed. A generator matrix for V can be taken to have the form [I 1 B], where BL = B. We enumerate and classify all circulant matrices B with this property. A number of open problems are listed.
منابع مشابه
An Efficient Construction of Self-Dual Codes
We complete the building-up construction for self-dual codes by resolving the open cases over GF (q) with q ≡ 3 (mod 4), and over Zpm and Galois rings GR(p, r) with an odd prime p satisfying p ≡ 3 (mod 4) with r odd. We also extend the buildingup construction for self-dual codes to finite chain rings. Our building-up construction produces many new interesting self-dual codes. In particular, we ...
متن کاملAn Upper Bound for Self-Dual Codes
Gleason has described the general form that the weight distribution of a self-dual code over GF(2) and GF(3) can have. We give an explicit formula for this weight distribution when the minimum distance d between codewords is made as large as possible. It follows that for self-dual codes of length n over GF(2) with all weights divisible by 4, d ~ 4[n/24] + 4; and for self-dual codes over GF(3), ...
متن کاملDirected graph representation of half-rate additive codes over GF(4)
Abstract. We show that (n, 2n) additive codes over GF(4) can be represented as directed graphs. This generalizes earlier results on self-dual additive codes over GF(4), which correspond to undirected graphs. Graph representation reduces the complexity of code classification, and enables us to classify additive (n, 2n) codes over GF(4) of length up to 7. From this we also derive classifications ...
متن کاملSpectral Orbits and Peak-to-Average Power Ratio of Boolean Functions with Respect to the {I, H, N}n Transform
We enumerate the inequivalent self-dual additive codes over GF(4) of blocklength n, thereby extending the sequence A090899 in The On-Line Encyclopedia of Integer Sequences from n = 9 to n = 12. These codes have a well-known interpretation as quantum codes. They can also be represented by graphs, where a simple graph operation generates the orbits of equivalent codes. We highlight the regularity...
متن کاملOn the Classification of Hermitian Self-Dual Additive Codes over GF(9)
Additive codes over GF(9) that are self-dual with respect to the Hermitian trace inner product have a natural application in quantum information theory, where they correspond to ternary quantum error-correcting codes. However, these codes have so far received far less interest from coding theorists than self-dual additive codes over GF(4), which correspond to binary quantum codes. Self-dual add...
متن کاملClassification of Hermitian self-dual additive codes over GF(9)
Abstract—Additive codes over GF(9) that are self-dual with respect to the Hermitian trace inner product have a natural application in quantum information theory, where they correspond to ternary quantum error-correcting codes. However, these codes have so far received far less interest from coding theorists than self-dual additive codes over GF(4), which correspond to binary quantum codes. 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:
- J. Comb. Theory, Ser. A
دوره 25 شماره
صفحات -
تاریخ انتشار 1978