A Lower Bound on the Weight Hierarchies of Product Codes
نویسندگان
چکیده
The weight of a code is the number of coordinate positions where not all codewords are zero. The rth minimum weight dr is the least weight of an r-dimensional subcode. Wei and Yang conjectured a formula for the minimum weights of some product codes, and this conjecture has recently been proved in two di2erent ways. In this self-contained paper, we give a further generalisation, with a new proof which also covers the old results. ? 2003 Elsevier Science B.V. All rights reserved.
منابع مشابه
A Lower Bound on the Greedy Weights of Product Codes
A greedy 1-subcode is a one-dimensional subcode of minimum (support) weight. A greedy r-subcode is an r-dimensional subcode with minimum support weight under the constraint that it contain a greedy (r − 1)-subcode. The r-th greedy weight er is the support weight of a greedy r-subcode. The greedy weights are related to the weight hierarchy. We use recent results on the weight hierarchy of produc...
متن کاملImproved Lower Bounds for the Error Rate of Linear Block Codes
Abstract We obtain two lower bounds on the error rate of linear binary block codes (under maximum likelihood decoding) over BPSK-modulated AWGN channels. We cast the problem of finding a lower bound on the probability of a union as an optimization problem which seeks to find the subset which maximizes a recent lower bound – due to Kuai, Alajaji, and Takahara – that we will refer to as the KAT b...
متن کاملOn Linear Codes over Z2s
In an earlier paper the authors studied simplex codes of type α and β over Z4 and obtained some known binary linear and nonlinear codes as Gray images of these codes. In this correspondence, we study weight distributions of simplex codes of type α and β over Z2s . The generalized Gray map is then used to construct binary codes. The linear codes meet the Griesmer bound and a few non-linear codes...
متن کاملOn Weight Hierarchies of Product Codes The Wei-Yang Conjecture and more
The weight of a code is the number of coordinate positions where no codeword is zero. The rth minimum weight dr is the least weight of an r-dimensional subcode. Wei and Yang conjectured a formula for the minimum weights of some product codes. The conjecture is proved in two di erent ways, each with interesting side-results.
متن کاملAn Algorithm Based on Theory of Constraints and Branch and Bound for Solving Integrated Product-Mix-Outsourcing Problem
One of the most important decision making problems in many production systems is identification and determination of products and their quantities according to available resources. This problem is called product-mix. However, in the real-world situations, for existing constrained resources, many companies try to provide some products from external resources to achieve more profits. In this pape...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Discrete Applied Mathematics
دوره 128 شماره
صفحات -
تاریخ انتشار 2003