In this letter, we consider the incorrigible sets of binary linear codes. First, we show that the incorrigible set enumerator of a binary linear code is tantamount to the Tutte polynomial of the vector matroid induced by the parity-check matrix of the code. A direct consequence is that determining the incorrigible set enumerator of binary linear codes is #P-hard. Then for a cycle code, we express its incorrigible set enumerator via the Tutte polynomial of the graph describing the code. Furthermore, we provide the explicit formula of incorrigible set enumerators of cycle codes constructed from complete graphs.
Hedong HOU
Tsinghua University
Haiyang LIU
the Institute of Microelectronics of Chinese Academy of Sciences
Lianrong MA
Tsinghua University
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Hedong HOU, Haiyang LIU, Lianrong MA, "Some Results on Incorrigible Sets of Binary Linear Codes" in IEICE TRANSACTIONS on Fundamentals,
vol. E104-A, no. 2, pp. 582-586, February 2021, doi: 10.1587/transfun.2020EAL2021.
Abstract: In this letter, we consider the incorrigible sets of binary linear codes. First, we show that the incorrigible set enumerator of a binary linear code is tantamount to the Tutte polynomial of the vector matroid induced by the parity-check matrix of the code. A direct consequence is that determining the incorrigible set enumerator of binary linear codes is #P-hard. Then for a cycle code, we express its incorrigible set enumerator via the Tutte polynomial of the graph describing the code. Furthermore, we provide the explicit formula of incorrigible set enumerators of cycle codes constructed from complete graphs.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2020EAL2021/_p
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@ARTICLE{e104-a_2_582,
author={Hedong HOU, Haiyang LIU, Lianrong MA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Some Results on Incorrigible Sets of Binary Linear Codes},
year={2021},
volume={E104-A},
number={2},
pages={582-586},
abstract={In this letter, we consider the incorrigible sets of binary linear codes. First, we show that the incorrigible set enumerator of a binary linear code is tantamount to the Tutte polynomial of the vector matroid induced by the parity-check matrix of the code. A direct consequence is that determining the incorrigible set enumerator of binary linear codes is #P-hard. Then for a cycle code, we express its incorrigible set enumerator via the Tutte polynomial of the graph describing the code. Furthermore, we provide the explicit formula of incorrigible set enumerators of cycle codes constructed from complete graphs.},
keywords={},
doi={10.1587/transfun.2020EAL2021},
ISSN={1745-1337},
month={February},}
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TY - JOUR
TI - Some Results on Incorrigible Sets of Binary Linear Codes
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 582
EP - 586
AU - Hedong HOU
AU - Haiyang LIU
AU - Lianrong MA
PY - 2021
DO - 10.1587/transfun.2020EAL2021
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E104-A
IS - 2
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - February 2021
AB - In this letter, we consider the incorrigible sets of binary linear codes. First, we show that the incorrigible set enumerator of a binary linear code is tantamount to the Tutte polynomial of the vector matroid induced by the parity-check matrix of the code. A direct consequence is that determining the incorrigible set enumerator of binary linear codes is #P-hard. Then for a cycle code, we express its incorrigible set enumerator via the Tutte polynomial of the graph describing the code. Furthermore, we provide the explicit formula of incorrigible set enumerators of cycle codes constructed from complete graphs.
ER -