Totally Disjoint 3-Digit Decimal Check Digit Codes
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918108296380416 |
|---|---|
| author | Dunning, Larry A. |
| author_facet | Dunning, Larry A. |
| contents | In 1969 J. Verhoeff provided the first examples of a decimal error detecting code using a single check digit to provide protection against all single, transposition and adjacent twin errors. The three versions of such a code that he presented are length 3-digit codes with 2 information digits. Existence of a 4-digit code would imply the existence of 10 such disjoint 3-digit codes. This paper presents 3 pairwise disjoint 3-digit codes. The codes developed herein, have the property that the knowledge of the multiset of digits included in a word is sufficient to determine the entire codeword even though their positions were unknown. Thus the codes are permutation-free, and this fulfills Verhoeff's desire to eliminate "cyclic errors". Phonetic errors, where 2 digit pairs of the forms X0 and 1X are interchanged, are also eliminated. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_05326 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Totally Disjoint 3-Digit Decimal Check Digit Codes Dunning, Larry A. Information Theory Combinatorics 68P30, 94B25, 05B15, 05B40, 20N15 H.1.1; G.2.1; F.2.1 In 1969 J. Verhoeff provided the first examples of a decimal error detecting code using a single check digit to provide protection against all single, transposition and adjacent twin errors. The three versions of such a code that he presented are length 3-digit codes with 2 information digits. Existence of a 4-digit code would imply the existence of 10 such disjoint 3-digit codes. This paper presents 3 pairwise disjoint 3-digit codes. The codes developed herein, have the property that the knowledge of the multiset of digits included in a word is sufficient to determine the entire codeword even though their positions were unknown. Thus the codes are permutation-free, and this fulfills Verhoeff's desire to eliminate "cyclic errors". Phonetic errors, where 2 digit pairs of the forms X0 and 1X are interchanged, are also eliminated. |
| title | Totally Disjoint 3-Digit Decimal Check Digit Codes |
| topic | Information Theory Combinatorics 68P30, 94B25, 05B15, 05B40, 20N15 H.1.1; G.2.1; F.2.1 |
| url | https://arxiv.org/abs/2504.05326 |