منابع مشابه
Ternary trades and their codes
In this paper, the notion of trades over finite fields is introduced. In particular, trades over GF (3) (ternary trades) are studied. By considering the incidence matrix of t-subsets vs. k-subsets of a v-set as a parity check matrix of a ternary code, we obtain a new family of codes in which every codeword is a ternary trade. The spectrum of weights of these codes is discussed; a simple and fas...
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In this paper we describe two classes of ternary codes, determine their minimum weight and weight distribution, and prove their properties. We also present four classes of 1-designs that are based on the classes of ternary codes.
متن کاملA class of optimal ternary cyclic codes and their duals
Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. Let m = 2l+1 for an integer l≥ 1 and π be a generator of GF(3m)∗. In this paper, a class of cyclic codes C(u,v) over GF(3) with two nonzeros πu and πv is studied, where u = (3m +1)/2, and v = 2 ·3l+ 1 ...
متن کاملTernary codes through ternary designs
It is known that under certain conditions the incidence matrix of a balanced incomplete block design (v, b, r, k, λ) gives a binary code of length b and size 2(v + 1). Here we investigate the conditions where a balanced ternary design gives a similar ternary code.
متن کاملTernary Linear Codes and Quadrics
For an [n, k, d]3 code C with gcd(d, 3) = 1, we define a map wG from Σ = PG(k − 1, 3) to the set of weights of codewords of C through a generator matrix G. A t-flat Π in Σ is called an (i, j)t flat if (i, j) = (|Π ∩ F0|, |Π ∩ F1|), where F0 = {P ∈ Σ | wG(P ) ≡ 0 (mod 3)}, F1 = {P ∈ Σ | wG(P ) 6≡ 0, d (mod 3)}. We give geometric characterizations of (i, j)t flats, which involve quadrics. As an a...
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ژورنال
عنوان ژورنال: Journal of Statistical Planning and Inference
سال: 2001
ISSN: 0378-3758
DOI: 10.1016/s0378-3758(00)00291-3