| Presentation | 1999/5/18 Approximating the maximum Weight of Linear Codes is APX-complete TOSHIYA ITOH, |
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| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | The minimum distance of a linear code C is a useful metric property for estimating the error correction upper bound of C and the maximum likelihood decoding of a linear code C is also of practical and theoretical importance. These problems are known to be NP-hard and are NP-hard to approximate within any constant factor to the optimum. As a problem related to the above, we consider the maximization problem MAX-WEIGHT: Given a generating matrix of a linear code C, find a codeword c∈C with its weight as close to the maximum weight of C as possible. It is shown that MAX-WEIGHT notin PTAS unless P = NP, however, no nontrivial approximation upper and lower bounds are known. In this paper, we investigate the complexity of MAX-WEIGHT to make the approximation upper and lower bounds more precise, and then show that (1) MAX-WEIGHT is APX-compete; (2) MAX-WEIGHT is 2-approximable; and (3) MAX-WEIGHT is not (10/9)-approximable unless P = NP. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | Approximation Algorithms / APX-complete / Maximum Weight / Linear Codes |
| Paper # | IT99-10 |
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| Conference Information | |
| Committee | IT |
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| Conference Date | 1999/5/18(1days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | |
| Topics (in Japanese) | (See Japanese page) |
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| Paper Information | |
| Registration To | Information Theory (IT) |
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| Language | ENG |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Approximating the maximum Weight of Linear Codes is APX-complete |
| Sub Title (in English) | |
| Keyword(1) | Approximation Algorithms |
| Keyword(2) | APX-complete |
| Keyword(3) | Maximum Weight |
| Keyword(4) | Linear Codes |
| 1st Author's Name | TOSHIYA ITOH |
| 1st Author's Affiliation | Department of Information Processing Interdisciplinary Graduate School of Science and Engineering Tokyo Institute of Technology() |
| Date | 1999/5/18 |
| Paper # | IT99-10 |
| Volume (vol) | vol.99 |
| Number (no) | 56 |
| Page | pp.pp.- |
| #Pages | 8 |
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